TSTP Solution File: SWV921-1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV921-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:19:25 EDT 2023

% Result   : Unsatisfiable 19.46s 5.64s
% Output   : Refutation 20.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  911
% Syntax   : Number of formulae    : 1690 ( 791 unt; 133 typ;   0 def)
%            Number of atoms       : 2653 (1388 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives : 67530 (1372   ~;1096   |;   0   &;65062   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   42 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  354 ( 354   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  135 ( 133 usr;  23 con; 0-6 aty)
%            Number of variables   : 8036 (   0   ^;8036   !;   0   ?;8036   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Conform_Olconf_type,type,
    c_Conform_Olconf: $i > $i > $i > $i > $i > $o ).

thf(v_P_type,type,
    v_P: $i ).

thf(c_Fun_Ofun__upd_type,type,
    c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).

thf(v_ha_______type,type,
    v_ha______: $i ).

thf(v_a_______type,type,
    v_a______: $i ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(c_Option_Ooption_OSome_type,type,
    c_Option_Ooption_OSome: $i > $i ).

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

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

thf(tc_String_Ochar_type,type,
    tc_String_Ochar: $i ).

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

thf(tc_Option_Ooption_type,type,
    tc_Option_Ooption: $i > $i ).

thf(tc_Value_Oval_type,type,
    tc_Value_Oval: $i ).

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

thf(v_C_______type,type,
    v_C______: $i ).

thf(v_fs_______type,type,
    v_fs______: $i ).

thf(v_F_______type,type,
    v_F______: $i ).

thf(v_D_______type,type,
    v_D______: $i ).

thf(v_v_______type,type,
    v_v______: $i ).

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

thf(v_la_______type,type,
    v_la______: $i ).

thf(v_E_____type,type,
    v_E____: $i ).

thf(tc_Expr_Oexp_type,type,
    tc_Expr_Oexp: $i > $i ).

thf(c_Expr_Oexp_OFAcc_type,type,
    c_Expr_Oexp_OFAcc: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OCond_type,type,
    c_Expr_Oexp_OCond: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OBlock_type,type,
    c_Expr_Oexp_OBlock: $i > $i > $i > $i > $i ).

thf(c_Fun_Oinj__on_type,type,
    c_Fun_Oinj__on: $i > $i > $i > $i > $o ).

thf(c_Fun_Oswap_type,type,
    c_Fun_Oswap: $i > $i > $i > $i > $i > $i ).

thf(hBOOL_type,type,
    hBOOL: $i > $o ).

thf(c_in_type,type,
    c_in: $i > $i > $i > $i ).

thf(c_Expr_Oexp_OVal_type,type,
    c_Expr_Oexp_OVal: $i > $i > $i ).

thf(c_Expr_Oexp_OVar_type,type,
    c_Expr_Oexp_OVar: $i > $i > $i ).

thf(c_Expr_Oexp_OLAss_type,type,
    c_Expr_Oexp_OLAss: $i > $i > $i > $i ).

thf(c_Expr_Oexp_OBinOp_type,type,
    c_Expr_Oexp_OBinOp: $i > $i > $i > $i > $i ).

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

thf(c_Expr_Oexp_OFAss_type,type,
    c_Expr_Oexp_OFAss: $i > $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OTryCatch_type,type,
    c_Expr_Oexp_OTryCatch: $i > $i > $i > $i > $i > $i ).

thf(c_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).

thf(c_Set_Oinsert_type,type,
    c_Set_Oinsert: $i > $i > $i > $i ).

thf(c_Orderings_Obot__class_Obot_type,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

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

thf(c_Expr_Oexp_OSeq_type,type,
    c_Expr_Oexp_OSeq: $i > $i > $i > $i ).

thf(c_Expr_Oexp_OWhile_type,type,
    c_Expr_Oexp_OWhile: $i > $i > $i > $i ).

thf(c_Expr_Oexp_Othrow_type,type,
    c_Expr_Oexp_Othrow: $i > $i > $i ).

thf(c_Expr_Oexp_OCall_type,type,
    c_Expr_Oexp_OCall: $i > $i > $i > $i > $i ).

thf(c_Set_Oimage_type,type,
    c_Set_Oimage: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1_type,type,
    c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OCast_type,type,
    c_Expr_Oexp_OCast: $i > $i > $i > $i ).

thf(c_Map_Omap__add_type,type,
    c_Map_Omap__add: $i > $i > $i > $i > $i ).

thf(c_Map_Omap__le_type,type,
    c_Map_Omap__le: $i > $i > $i > $i > $o ).

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

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

thf(c_Exceptions_Opreallocated_type,type,
    c_Exceptions_Opreallocated: $i > $o ).

thf(c_Objects_Ohext_type,type,
    c_Objects_Ohext: $i > $i > $o ).

thf(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2_type,type,
    c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2: $i > $i > $i > $i > $i > $i ).

thf(c_Fun_Othe__inv__into_type,type,
    c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).

thf(c_Option_Ois__none_type,type,
    c_Option_Ois__none: $i > $i > $i ).

thf(c_Option_Ooption_ONone_type,type,
    c_Option_Ooption_ONone: $i > $i ).

thf(class_Orderings_Obot_type,type,
    class_Orderings_Obot: $i > $o ).

thf(c_Fun_Ocomp_type,type,
    c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).

thf(c_Fun_Oid_type,type,
    c_Fun_Oid: $i > $i ).

thf(c_Value_Oval_OAddr_type,type,
    c_Value_Oval_OAddr: $i > $i ).

thf(c_Value_Oval_OUnit_type,type,
    c_Value_Oval_OUnit: $i ).

thf(c_Product__Type_Oapsnd_type,type,
    c_Product__Type_Oapsnd: $i > $i > $i > $i ).

thf(c_Product__Type_Oprod__fun_type,type,
    c_Product__Type_Oprod__fun: $i > $i > $i > $i > $i > $i ).

thf(c_Option_Ooption_Ooption__case_type,type,
    c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).

thf(c_fequal_type,type,
    c_fequal: $i > $i > $i > $i ).

thf(class_OrderedGroup_Oab__group__add_type,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

thf(c_COMBK_type,type,
    c_COMBK: $i > $i > $i > $i ).

thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

thf(c_Finite__Set_Osetprod_type,type,
    c_Finite__Set_Osetprod: $i > $i > $i > $i > $i ).

thf(c_Hilbert__Choice_Oinv__into_type,type,
    c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).

thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

thf(c_Finite__Set_Osetsum_type,type,
    c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).

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

thf(c_COMBI_type,type,
    c_COMBI: $i > $i ).

thf(c_Conform_Ooconf_type,type,
    c_Conform_Ooconf: $i > $i > $i > $i > $o ).

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

thf(class_Orderings_Otop_type,type,
    class_Orderings_Otop: $i > $o ).

thf(c_Map_Omap__upds_type,type,
    c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).

thf(c_Option_Ooption_Ooption__rec_type,type,
    c_Option_Ooption_Ooption__rec: $i > $i > $i > $i > $i > $i ).

thf(c_Product__Type_Oprod_Oprod__case_type,type,
    c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).

thf(c_split_type,type,
    c_split: $i > $i > $i > $i ).

thf(c_Conform_Oconf_type,type,
    c_Conform_Oconf: $i > $i > $i > $i > $i > $o ).

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

thf(c_Product__Type_Ointernal__split_type,type,
    c_Product__Type_Ointernal__split: $i > $i > $i > $i ).

thf(c_Conform_Ohconf_type,type,
    c_Conform_Ohconf: $i > $i > $i > $o ).

thf(c_WellTypeRT_OWTrt_type,type,
    c_WellTypeRT_OWTrt: $i > $i > $i > $i > $i > $o ).

thf(c_Conform_Osko__Conform__Xhconf__def__1__2_type,type,
    c_Conform_Osko__Conform__Xhconf__def__1__2: $i > $i > $i > $i ).

thf(c_SmallStep_Ored_type,type,
    c_SmallStep_Ored: $i > $i ).

thf(c_Orderings_Otop__class_Otop_type,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

thf(c_SmallStep_Oredp_type,type,
    c_SmallStep_Oredp: $i > $i > $i > $i > $i > $o ).

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

thf(v_x_type,type,
    v_x: $i ).

thf(c_curry_type,type,
    c_curry: $i > $i > $i > $i > $i ).

thf(c_State_Ohp_type,type,
    c_State_Ohp: $i > $i > $i ).

thf(t_b_type,type,
    t_b: $i ).

thf(v_sko__Option__Xoption__Xsplit__1_type,type,
    v_sko__Option__Xoption__Xsplit__1: $i > $i > $i > $i ).

thf(c_Product__Type_Oscomp_type,type,
    c_Product__Type_Oscomp: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Product__Type_Oprod_Oprod__rec_type,type,
    c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).

thf(c_Map_Orestrict__map_type,type,
    c_Map_Orestrict__map: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Option__Xospec__1__1_type,type,
    c_ATP__Linkup_Osko__Option__Xospec__1__1: $i > $i > $i > $i ).

thf(v_sko__Option__Xoption__Xsplit__asm__1_type,type,
    v_sko__Option__Xoption__Xsplit__asm__1: $i > $i > $i > $i ).

thf(c_Option_Omap_type,type,
    c_Option_Omap: $i > $i > $i > $i ).

thf(c_Product__Type_Oapfst_type,type,
    c_Product__Type_Oapfst: $i > $i > $i > $i > $i ).

thf(c_Fun_Ooverride__on_type,type,
    c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1_type,type,
    c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Ofilter_type,type,
    c_List_Ofilter: $i > $i > $i > $i ).

thf(c_Map_Omap__comp_type,type,
    c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).

thf(tc_Type_Oty_type,type,
    tc_Type_Oty: $i ).

thf(c_Conform_Osko__Conform__Xlconf__def__1__1_type,type,
    c_Conform_Osko__Conform__Xlconf__def__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Map_Omap__of_type,type,
    c_Map_Omap__of: $i > $i > $i > $i ).

thf(c_Objects_Otypeof__h_type,type,
    c_Objects_Otypeof__h: $i > $i > $i ).

thf(c_BigStep_Oeval_type,type,
    c_BigStep_Oeval: $i > $i > $i > $i > $i > $o ).

thf(c_Map_Odom_type,type,
    c_Map_Odom: $i > $i > $i > $i ).

thf(c_Option_Oset_type,type,
    c_Option_Oset: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__Ex__1__3_type,type,
    c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__Ex__1__3: $i > $i > $i > $i ).

thf(v_T_____type,type,
    v_T____: $i ).

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

thf(c_Nat_Osize__class_Osize_type,type,
    c_Nat_Osize__class_Osize: $i > $i > $i ).

thf(c_Map_Oran_type,type,
    c_Map_Oran: $i > $i > $i > $i ).

thf(c_Map_Osko__Map__Xmap__comp__None__iff__1__1_type,type,
    c_Map_Osko__Map__Xmap__comp__None__iff__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_TypeRel_Ohas__field_type,type,
    c_TypeRel_Ohas__field: $i > $i > $i > $i > $i > $i > $o ).

thf(c_Objects_Osko__Objects__Xhext__objD__1__1_type,type,
    c_Objects_Osko__Objects__Xhext__objD__1__1: $i > $i > $i > $i ).

thf(c_State_Olcl_type,type,
    c_State_Olcl: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__All__1__1_type,type,
    c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__All__1__1: $i > $i > $i > $i ).

thf(c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1_type,type,
    c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1: $i > $i > $i > $i > $i ).

thf(c_Option_Othe_type,type,
    c_Option_Othe: $i > $i > $i ).

thf(v_xa_type,type,
    v_xa: $i ).

thf(c_Objects_Osko__Objects__Xhext__def__1__1_type,type,
    c_Objects_Osko__Objects__Xhext__def__1__1: $i > $i > $i > $i ).

thf(t_c_type,type,
    t_c: $i ).

thf(c_Conform_Osko__Conform__Xlconf__def__1__2_type,type,
    c_Conform_Osko__Conform__Xlconf__def__1__2: $i > $i > $i > $i > $i > $i ).

thf(c_Conform_Osko__Conform__Xlconf__def__1__3_type,type,
    c_Conform_Osko__Conform__Xlconf__def__1__3: $i > $i > $i > $i > $i > $i ).

thf(529,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_Option_Omap @ A @ B @ C ) @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ t_a ) @ ( tc_Option_Ooption @ B ) @ ( tc_Option_Ooption @ C ) @ t_a ) @ v_x )
      = ( c_Option_Ooption_ONone @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__o__empty_0) ).

thf(2163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_Option_Omap @ A @ B @ C ) @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ t_a ) @ ( tc_Option_Ooption @ B ) @ ( tc_Option_Ooption @ C ) @ t_a ) @ v_x )
      = ( c_Option_Ooption_ONone @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(189,axiom,
    class_HOL_Ominus @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(1322,plain,
    class_HOL_Ominus @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(252,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I158_J_0) ).

thf(1501,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(221,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).

thf(1411,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(377,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) @ D @ ( tc_prod @ A @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(1823,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) @ D @ ( tc_prod @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Option__Xospec__1__1 @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ C ) @ A @ B ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ospec_1) ).

thf(1767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Option__Xospec__1__1 @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ C ) @ A @ B ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(272,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).

thf(1559,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).

thf(941,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(581,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ D ) @ B @ ( tc_Option_Ooption @ A ) ) @ B @ A )
      = ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_1) ).

thf(2280,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ D ) @ B @ ( tc_Option_Ooption @ A ) ) @ B @ A )
      = ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(317,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow2_0) ).

thf(1686,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(729,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(2612,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(241,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I92_J_0) ).

thf(1469,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(139,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

thf(1168,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(588,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( D
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

thf(2295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( D
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(593,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(2306,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(515,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_Conform_Olconf @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lconf__hext_0) ).

thf(2131,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_Conform_Olconf @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(468,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OFAssThrow1_0) ).

thf(2031,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(638,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ F @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ B @ F @ D ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upd_0) ).

thf(2412,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ F @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ B @ F @ D ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(23,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_0) ).

thf(846,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(45,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).

thf(909,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_OUnit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I11_J_0) ).

thf(1031,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_OUnit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(660,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).

thf(2463,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(410,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Option_Oset @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_Option_Ooption_ONone @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty__eq_0) ).

thf(1899,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Option_Oset @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_Option_Ooption_ONone @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(722,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OBlockThrow_0) ).

thf(2595,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(677,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).

thf(2499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(646,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(2427,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(448,axiom,
    ( ( c_Option_Ois__none @ v_x @ t_a )
    = ( c_fequal @ v_x @ ( c_Option_Ooption_ONone @ t_a ) @ ( tc_Option_Ooption @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__none__def__raw_0) ).

thf(1982,plain,
    ( ( c_Option_Ois__none @ v_x @ t_a )
    = ( c_fequal @ v_x @ ( c_Option_Ooption_ONone @ t_a ) @ ( tc_Option_Ooption @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(436,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OInitBlockThrow_0) ).

thf(1956,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(269,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I149_J_0) ).

thf(1549,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1211,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(594,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ( B = C )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(2309,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ( B = C )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(80,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).

thf(1005,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(509,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(2117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(675,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_curry @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ A @ B @ C )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curry__split_0) ).

thf(2495,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_curry @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ A @ B @ C )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(749,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).

thf(2659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(427,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1939,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(336,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ A ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ B ) @ E ) @ ( hAPP @ D @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__conv_0) ).

thf(1728,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ A ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ B ) @ E ) @ ( hAPP @ D @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(624,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ~ ( c_Conform_Oconf @ D @ E @ F @ C @ G )
      | ~ ( c_Conform_Olconf @ D @ E @ H @ A @ G )
      | ( c_Conform_Olconf @ D @ E @ ( c_Fun_Ofun__upd @ H @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) @ A @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lconf__upd_0) ).

thf(2380,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ~ ( c_Conform_Oconf @ D @ E @ F @ C @ G )
      | ~ ( c_Conform_Olconf @ D @ E @ H @ A @ G )
      | ( c_Conform_Olconf @ D @ E @ ( c_Fun_Ofun__upd @ H @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) @ A @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

thf(1692,plain,
    ! [A: $i] :
      ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).

thf(1437,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(617,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( hBOOL @ ( c_in @ F @ ( c_List_Oset @ B @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__apply__nontin_0) ).

thf(2363,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( hBOOL @ ( c_in @ F @ ( c_List_Oset @ B @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(390,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OSeqThrow_0) ).

thf(1855,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(490,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).

thf(2077,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(76,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
      | ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).

thf(994,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
      | ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(692,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(2527,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(756,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(2671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(758,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ ( c_Fun_Ofun__upd @ F @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__upd_0) ).

thf(2676,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ ( c_Fun_Ofun__upd @ F @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(32,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).

thf(873,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(152,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).

thf(1205,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(500,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastRedsThrow_0) ).

thf(2099,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(582,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      | ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(2282,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      | ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(283,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_snd @ A @ B @ C )
       != ( c_snd @ D @ B @ C ) )
      | ( ( c_fst @ A @ B @ C )
       != ( c_fst @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__eqI_0) ).

thf(1591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_snd @ A @ B @ C )
       != ( c_snd @ D @ B @ C ) )
      | ( ( c_fst @ A @ B @ C )
       != ( c_fst @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(443,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).

thf(1971,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(364,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ B @ C @ D ) )
      | ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_1) ).

thf(1793,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ B @ C @ D ) )
      | ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(264,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).

thf(1533,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(362,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).

thf(1788,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(311,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).

thf(1671,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ A @ B @ C @ D )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_swap__self_0) ).

thf(1655,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ A @ B @ C @ D )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(763,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oapfst @ A @ B @ C @ D )
      = ( hAPP @ ( c_Product__Type_Oprod__fun @ A @ B @ C @ D @ D ) @ ( c_Fun_Oid @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apfst__def_0) ).

thf(2686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oapfst @ A @ B @ C @ D )
      = ( hAPP @ ( c_Product__Type_Oprod__fun @ A @ B @ C @ D @ D ) @ ( c_Fun_Oid @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(339,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ E @ A @ C ) @ F ) @ G ) )
      = ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ E @ B @ C ) @ ( c_Fun_Ocomp @ D @ F @ A @ B @ E ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__compose_0) ).

thf(1735,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ E @ A @ C ) @ F ) @ G ) )
      = ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ E @ B @ C ) @ ( c_Fun_Ocomp @ D @ F @ A @ B @ E ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(540,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Map_Odom @ B @ C @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).

thf(2184,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Map_Odom @ B @ C @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(655,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(2448,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(174,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

thf(1275,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(532,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).

thf(2168,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(58,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).

thf(945,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(201,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).

thf(1354,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(237,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      | ~ ( c_Map_Omap__le @ B @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).

thf(1458,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      | ~ ( c_Map_Omap__le @ B @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(714,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedBlock_0) ).

thf(2575,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(251,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).

thf(1497,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(544,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Map_Odom @ A @ B @ C ) @ B @ ( tc_Option_Ooption @ C ) )
      | ~ ( c_Fun_Oinj__on @ ( c_Map_Omap__add @ D @ A @ B @ C ) @ ( c_Map_Odom @ A @ B @ C ) @ B @ ( tc_Option_Ooption @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__map__add__dom_0) ).

thf(2195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Map_Odom @ A @ B @ C ) @ B @ ( tc_Option_Ooption @ C ) )
      | ~ ( c_Fun_Oinj__on @ ( c_Map_Omap__add @ D @ A @ B @ C ) @ ( c_Map_Odom @ A @ B @ C ) @ B @ ( tc_Option_Ooption @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(348,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__in_0) ).

thf(1756,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(185,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).

thf(1310,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(455,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Map_Oran @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ran__empty_0) ).

thf(1999,plain,
    ! [B: $i,A: $i] :
      ( ( c_Map_Oran @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(597,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).

thf(2316,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(254,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).

thf(1507,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(616,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(2360,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(553,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( D = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).

thf(2216,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( D = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(610,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed2_0) ).

thf(2348,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(475,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed1_0) ).

thf(2046,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(416,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(1914,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(214,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).

thf(1391,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(231,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).

thf(1441,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(463,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_split @ E @ F @ ( tc_fun @ G @ tc_bool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ E @ F ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_H_0) ).

thf(2020,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_split @ E @ F @ ( tc_fun @ G @ tc_bool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ E @ F ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I127_J_0) ).

thf(973,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(425,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_fst @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ E ) @ C @ B )
      = ( c_fst @ E @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__apsnd_0) ).

thf(1935,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_fst @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ E ) @ C @ B )
      = ( c_fst @ E @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(302,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_0) ).

thf(1645,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(243,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I104_J_0) ).

thf(1475,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(534,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ E @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ E @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).

thf(2173,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ E @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ E @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(368,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(1803,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(246,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).

thf(1482,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(1887,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(18,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).

thf(829,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).

thf(1095,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(344,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oprod_Oprod__rec @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C @ F )
      = ( hAPP @ ( hAPP @ A @ D ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod_Orecs_0) ).

thf(1746,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oprod_Oprod__rec @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C @ F )
      = ( hAPP @ ( hAPP @ A @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).

thf(898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(700,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ E @ ( tc_prod @ A @ B ) ) @ A @ B ) @ C )
      = ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of__Cons__code_I2_J_0) ).

thf(2548,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ E @ ( tc_prod @ A @ B ) ) @ A @ B ) @ C )
      = ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(1782,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(412,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ D @ E ) @ D ) )
      | ~ ( c_Map_Omap__le @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__def_0) ).

thf(1904,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ D @ E ) @ D ) )
      | ~ ( c_Map_Omap__le @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(259,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).

thf(1518,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(171,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).

thf(1265,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(325,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( c_State_Ohp @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ H @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccRedsVal_0) ).

thf(1703,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( c_State_Ohp @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ H @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVar @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I133_J_0) ).

thf(1628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVar @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(178,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

thf(1287,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(328,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ B @ tc_bool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__caseI_0) ).

thf(1709,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ B @ tc_bool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(726,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
      | ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) )
        = ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) )
      | ( ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) ) )
        = ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_4) ).

thf(2603,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
      | ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) )
        = ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) )
      | ( ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) ) )
        = ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(1430,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(472,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(2039,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(754,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ G @ ( tc_Option_Ooption @ C ) ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).

thf(2667,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ G @ ( tc_Option_Ooption @ C ) ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(576,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Set_Oimage @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

thf(2269,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Set_Oimage @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(397,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqRedsThrow_0) ).

thf(1871,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(773,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).

thf(2708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(413,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      | ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ ( hAPP @ A @ D ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).

thf(1907,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      | ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ ( hAPP @ A @ D ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
        = A )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
        = A )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(9,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I128_J_0) ).

thf(802,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(761,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ofun__upd @ B @ C @ D @ E @ F ) @ F @ G @ E )
      = ( c_Fun_Ofun__upd @ ( c_Fun_Ocomp @ A @ B @ F @ G @ E ) @ C @ ( hAPP @ A @ D ) @ E @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__comp_0) ).

thf(2682,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ofun__upd @ B @ C @ D @ E @ F ) @ F @ G @ E )
      = ( c_Fun_Ofun__upd @ ( c_Fun_Ocomp @ A @ B @ F @ G @ E ) @ C @ ( hAPP @ A @ D ) @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(186,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).

thf(1313,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(236,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I223_J_0) ).

thf(1455,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(708,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Conform_Ooconf @ E @ A @ F @ G )
      | ( c_Conform_Ooconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ H ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_oconf__upd__obj_0) ).

thf(2562,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Conform_Ooconf @ E @ A @ F @ G )
      | ( c_Conform_Ooconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ H ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(452,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1992,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(127,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).

thf(1132,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(712,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ A @ B @ tc_bool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitI_0) ).

thf(2571,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ A @ B @ tc_bool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(770,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_elem__set_1) ).

thf(2703,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(768,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ ( c_fst @ A @ B @ C ) ) @ ( c_snd @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surjective__pairing_0) ).

thf(2698,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ ( c_fst @ A @ B @ C ) ) @ ( c_snd @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(350,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow1_0) ).

thf(1760,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(192,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).

thf(1330,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(653,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ ( c_Option_Ooption_ONone @ A ) @ t_a @ ( tc_Option_Ooption @ A ) ) @ v_xa )
      = ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__upd__none_0) ).

thf(2444,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ ( c_Option_Ooption_ONone @ A ) @ t_a @ ( tc_Option_Ooption @ A ) ) @ v_xa )
      = ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(392,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ D @ E @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ E ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_0) ).

thf(1860,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ D @ E @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ E ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(578,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(2274,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(48,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).

thf(917,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(642,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OCallThrowObj_0) ).

thf(2420,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(132,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I119_J_0) ).

thf(1147,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(702,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds2_0) ).

thf(2552,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I116_J_0) ).

thf(1572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__rec @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Orecs_I1_J_0) ).

thf(1398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__rec @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(121,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ E )
      | ( ( c_Finite__Set_Osetprod @ F @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ A )
        = ( c_Finite__Set_Osetprod @ ( c_Fun_Ocomp @ F @ B @ E @ A @ D ) @ C @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__reindex__cong_0) ).

thf(1115,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ E )
      | ( ( c_Finite__Set_Osetprod @ F @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ A )
        = ( c_Finite__Set_Osetprod @ ( c_Fun_Ocomp @ F @ B @ E @ A @ D ) @ C @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(275,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).

thf(1568,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(465,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp2Reds_0) ).

thf(2024,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(250,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I102_J_0) ).

thf(1494,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(440,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_SmallStep_Oredp @ E @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ G @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ I ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) @ G ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ H ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ I ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedFAss_0) ).

thf(1963,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_SmallStep_Oredp @ E @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ G @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ I ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) @ G ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ H ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ I ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(161,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I70_J_0) ).

thf(1232,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(634,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_Ooption__case @ A @ B @ C @ D @ E )
        = ( c_Option_Ooption_Ooption__case @ A @ F @ C @ D @ E ) )
      | ( C
        = ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ C @ B @ F @ E @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Ocase__cong_2) ).

thf(2403,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_Ooption__case @ A @ B @ C @ D @ E )
        = ( c_Option_Ooption_Ooption__case @ A @ F @ C @ D @ E ) )
      | ( C
        = ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ C @ B @ F @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I203_J_0) ).

thf(1087,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(257,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).

thf(1514,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(188,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I88_J_0) ).

thf(1319,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
       != ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).

thf(870,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
       != ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(627,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

thf(2388,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(694,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( c_Option_Ooption_ONone @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_0) ).

thf(2533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( c_Option_Ooption_ONone @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(458,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(2007,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(536,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oscomp @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D @ B @ A @ B @ E )
      = ( hAPP @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__scomp_0) ).

thf(2178,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oscomp @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D @ B @ A @ B @ E )
      = ( hAPP @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).

thf(924,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(330,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Fun_Ofun__upd @ E @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      | ~ ( c_Map_Omap__le @ A @ E @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__imp__upd__le_0) ).

thf(1714,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Fun_Ofun__upd @ E @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      | ~ ( c_Map_Omap__le @ A @ E @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(234,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).

thf(1450,plain,
    ! [B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(496,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) @ D @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(2090,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) @ D @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(119,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I191_J_0) ).

thf(1109,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(572,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_Objects_Ohext @ A @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ E ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__upd__obj_0) ).

thf(2259,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_Objects_Ohext @ A @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ E ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(746,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ~ ( c_Conform_Ohconf @ C @ A @ D )
      | ( c_Conform_Ohconf @ C @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ D )
      | ~ ( c_Conform_Ooconf @ C @ A @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hconf__new_0) ).

thf(2650,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ~ ( c_Conform_Ohconf @ C @ A @ D )
      | ( c_Conform_Ohconf @ C @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ D )
      | ~ ( c_Conform_Ooconf @ C @ A @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(656,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__apply__notin_0) ).

thf(2451,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(394,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).

thf(1864,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(379,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(1828,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(704,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Val_0) ).

thf(2555,plain,
    ! [C: $i,B: $i,A: $i] : ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(462,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__upds @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ G @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__upds @ A @ F @ G @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ ( c_List_Oset @ F @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__twist_0) ).

thf(2017,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__upds @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ G @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__upds @ A @ F @ G @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ ( c_List_Oset @ F @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(248,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__upds @ B @ C @ D @ E @ F ) @ E @ F )
      = ( c_Map_Omap__upds @ ( c_Map_Omap__add @ A @ B @ E @ F ) @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upds_0) ).

thf(1489,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__upds @ B @ C @ D @ E @ F ) @ E @ F )
      = ( c_Map_Omap__upds @ ( c_Map_Omap__add @ A @ B @ E @ F ) @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(563,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_State_Olcl @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ A ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedVar_0) ).

thf(2237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_State_Olcl @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ A ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(1415,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(313,axiom,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(1677,plain,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(697,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OFAcc @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OFAccRed_0) ).

thf(2540,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OFAcc @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(470,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      | ( D = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(2034,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      | ( D = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(144,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I201_J_0) ).

thf(1183,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(177,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).

thf(1283,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(682,axiom,
    class_HOL_Ominus @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

thf(2508,plain,
    class_HOL_Ominus @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(542,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ D ) @ B @ E @ D ) @ C @ D @ E @ B )
        = A )
      | ~ ( c_Fun_Oinj__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__inv__o__cancel_0) ).

thf(2190,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ D ) @ B @ E @ D ) @ C @ D @ E @ B )
        = A )
      | ~ ( c_Fun_Oinj__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(1447,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(294,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I107_J_0) ).

thf(1622,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(518,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_Conform_Oconf @ E @ A @ F @ G @ H )
      | ~ ( c_Conform_Oconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ I ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ F @ G @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__upd__obj_0) ).

thf(2137,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_Conform_Oconf @ E @ A @ F @ G @ H )
      | ~ ( c_Conform_Oconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ I ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(502,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ H ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ I ) @ A ) ) ) @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ I ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ F @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OInitBlockRed_0) ).

thf(2103,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ H ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ I ) @ A ) ) ) @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ I ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ F @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ J ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(429,axiom,
    c_WellTypeRT_OWTrt @ v_P @ v_ha______ @ v_E____ @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ v_a______ ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_F______ @ v_D______ @ ( c_Expr_Oexp_OVal @ v_v______ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1943,plain,
    c_WellTypeRT_OWTrt @ v_P @ v_ha______ @ v_E____ @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ v_a______ ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_F______ @ v_D______ @ ( c_Expr_Oexp_OVal @ v_v______ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_fequal @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1600,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_fequal @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(549,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
        = ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).

thf(2205,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
        = ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(1696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(386,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( c_Conform_Olconf @ D @ E @ A @ F @ G )
      | ( ( hAPP @ F @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ ( c_Conform_Osko__Conform__Xlconf__def__1__1 @ F @ D @ B @ E @ C @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lconf__def_0) ).

thf(1843,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( c_Conform_Olconf @ D @ E @ A @ F @ G )
      | ( ( hAPP @ F @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ ( c_Conform_Osko__Conform__Xlconf__def__1__1 @ F @ D @ B @ E @ C @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(481,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

thf(2058,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(619,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_Fun_Oinj__on @ D @ B @ C @ E )
      | ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ D @ C @ E ) @ ( hAPP @ D @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).

thf(2367,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_Fun_Oinj__on @ D @ B @ C @ E )
      | ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ D @ C @ E ) @ ( hAPP @ D @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(650,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(2437,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ C @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedSeq_0) ).

thf(1928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ C @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(105,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).

thf(1072,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(693,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(2530,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(689,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(2523,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).

thf(1796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(73,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I50_J_0) ).

thf(988,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(584,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(2286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(741,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).

thf(2639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(117,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1104,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(164,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).

thf(1242,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_split @ A @ B @ C ) @ ( c_curry @ D @ A @ B @ C ) )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__curry_0) ).

thf(2154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_split @ A @ B @ C ) @ ( c_curry @ D @ A @ B @ C ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(260,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).

thf(1521,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(664,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ E ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ ( c_Fun_Ofun__upd @ E @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedLAss_0) ).

thf(2473,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ E ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ ( c_Fun_Ofun__upd @ E @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(6,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).

thf(793,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(744,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__comp @ A @ B @ C @ D @ E @ F )
       != ( c_Option_Ooption_ONone @ E ) )
      | ( ( hAPP @ B @ C )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ ( c_Map_Osko__Map__Xmap__comp__None__iff__1__1 @ C @ A @ B @ F @ D @ E ) ) )
      | ( ( hAPP @ B @ C )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__None__iff_0) ).

thf(2646,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__comp @ A @ B @ C @ D @ E @ F )
       != ( c_Option_Ooption_ONone @ E ) )
      | ( ( hAPP @ B @ C )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ ( c_Map_Osko__Map__Xmap__comp__None__iff__1__1 @ C @ A @ B @ F @ D @ E ) ) )
      | ( ( hAPP @ B @ C )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(134,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I95_J_0) ).

thf(1153,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(12,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).

thf(810,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(195,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).

thf(1338,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(327,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OInitBlockThrow_0) ).

thf(1708,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(742,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCall @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OCallObj_0) ).

thf(2641,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCall @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(337,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

thf(1730,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(493,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod__fun @ A @ B @ C @ D @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ D ) @ G ) @ H ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ E ) @ ( hAPP @ A @ G ) ) @ ( hAPP @ F @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__fun_0) ).

thf(2083,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod__fun @ A @ B @ C @ D @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ D ) @ G ) @ H ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ E ) @ ( hAPP @ A @ G ) ) @ ( hAPP @ F @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(734,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(2621,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(750,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__empty_0) ).

thf(2660,plain,
    ! [B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(396,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ B @ F ) )
      | ~ ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__apply__in_0) ).

thf(1868,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ B @ F ) )
      | ~ ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(483,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ F ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).

thf(2061,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ F ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(299,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I59_J_0) ).

thf(1636,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(652,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ C @ B @ D ) @ B @ D ) @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of__zip__is__None_1) ).

thf(2441,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ C @ B @ D ) @ B @ D ) @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(720,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).

thf(2589,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(158,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I164_J_0) ).

thf(1223,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(725,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowReds_0) ).

thf(2601,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(707,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).

thf(2560,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(568,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OSeq @ E @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ B @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OSeqRed_0) ).

thf(2249,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OSeq @ E @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ B @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(723,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(2596,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(168,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).

thf(1255,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(156,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Oswap @ A @ B @ ( c_Fun_Oswap @ B @ C @ ( c_Fun_Oswap @ A @ B @ D @ E @ F ) @ E @ F ) @ E @ F )
        = ( c_Fun_Oswap @ A @ C @ D @ E @ F ) )
      | ( B = C )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_swap__triple_0) ).

thf(1217,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Oswap @ A @ B @ ( c_Fun_Oswap @ B @ C @ ( c_Fun_Oswap @ A @ B @ D @ E @ F ) @ E @ F ) @ E @ F )
        = ( c_Fun_Oswap @ A @ C @ D @ E @ F ) )
      | ( B = C )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(346,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).

thf(1751,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ohconf @ A @ B @ C )
      | ~ ( c_Exceptions_Opreallocated @ B )
      | ~ ( c_Conform_Ooconf @ A @ B @ ( c_Conform_Osko__Conform__Xhconf__def__1__2 @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hconf__def_3) ).

thf(1666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ohconf @ A @ B @ C )
      | ~ ( c_Exceptions_Opreallocated @ B )
      | ~ ( c_Conform_Ooconf @ A @ B @ ( c_Conform_Osko__Conform__Xhconf__def__1__2 @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(727,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit__asm_2) ).

thf(2606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(2032,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(639,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ A @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__conv_0) ).

thf(2414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ A @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(631,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).

thf(2396,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(403,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ ( c_Option_Omap @ A @ B @ C ) @ ( c_Fun_Ofun__upd @ D @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ F ) @ G @ ( tc_Option_Ooption @ B ) ) @ ( tc_Option_Ooption @ B ) @ ( tc_Option_Ooption @ C ) @ G )
      = ( c_Fun_Ofun__upd @ ( c_Fun_Ocomp @ ( c_Option_Omap @ A @ B @ C ) @ D @ ( tc_Option_Ooption @ B ) @ ( tc_Option_Ooption @ C ) @ G ) @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ A @ F ) ) @ G @ ( tc_Option_Ooption @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__o__map__upd_0) ).

thf(1883,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ ( c_Option_Omap @ A @ B @ C ) @ ( c_Fun_Ofun__upd @ D @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ F ) @ G @ ( tc_Option_Ooption @ B ) ) @ ( tc_Option_Ooption @ B ) @ ( tc_Option_Ooption @ C ) @ G )
      = ( c_Fun_Ofun__upd @ ( c_Fun_Ocomp @ ( c_Option_Omap @ A @ B @ C ) @ D @ ( tc_Option_Ooption @ B ) @ ( tc_Option_Ooption @ C ) @ G ) @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ A @ F ) ) @ G @ ( tc_Option_Ooption @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(574,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(2264,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) @ ( tc_prod @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(637,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

thf(2409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).

thf(1042,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(61,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).

thf(952,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(124,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ F @ E ) @ G )
        = ( hAPP @ ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ A @ C @ F @ D ) @ ( c_Hilbert__Choice_Oinv__into @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ E ) @ D @ F @ E ) @ G ) )
      | ~ ( hBOOL @ ( c_in @ G @ ( c_Set_Oimage @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ C @ A @ F @ D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__comp_0) ).

thf(1123,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ F @ E ) @ G )
        = ( hAPP @ ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ A @ C @ F @ D ) @ ( c_Hilbert__Choice_Oinv__into @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ E ) @ D @ F @ E ) @ G ) )
      | ~ ( hBOOL @ ( c_in @ G @ ( c_Set_Oimage @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ C @ A @ F @ D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(28,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ ( c_Fun_Oswap @ E @ F @ A @ C @ D ) @ B @ C @ D )
      | ~ ( hBOOL @ ( c_in @ F @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__swap__iff_0) ).

thf(862,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ ( c_Fun_Oswap @ E @ F @ A @ C @ D ) @ B @ C @ D )
      | ~ ( hBOOL @ ( c_in @ F @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(141,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).

thf(1174,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(516,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ C @ A ) @ G ) )
      = ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ F ) @ D ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__apfst__commute_0) ).

thf(2133,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ C @ A ) @ G ) )
      = ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ F ) @ D ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(4,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Oswap @ A @ B @ C @ D @ E ) @ F @ D @ E )
      | ~ ( c_Fun_Oinj__on @ C @ F @ D @ E )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ F @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__swap__iff_1) ).

thf(788,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Oswap @ A @ B @ C @ D @ E ) @ F @ D @ E )
      | ~ ( c_Fun_Oinj__on @ C @ F @ D @ E )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ F @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(293,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).

thf(1619,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(207,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ ( c_Map_Omap__upds @ F @ B @ C @ D @ E ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__upds_0) ).

thf(1370,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ ( c_Map_Omap__upds @ F @ B @ C @ D @ E ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(163,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

thf(1238,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).

thf(2015,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oprod_Oprod__case @ A @ B @ C )
      = ( c_split @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__case__split_0) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oprod_Oprod__case @ A @ B @ C )
      = ( c_split @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(755,axiom,
    ! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Option_Ooption_OSome @ A ) @ B @ A @ ( tc_Option_Ooption @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__Some_0) ).

thf(2670,plain,
    ! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Option_Ooption_OSome @ A ) @ B @ A @ ( tc_Option_Ooption @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ~ ( c_Objects_Ohext @ A @ D )
      | ( ( c_Objects_Otypeof__h @ D @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__typeof__mono_0) ).

thf(1920,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ~ ( c_Objects_Ohext @ A @ D )
      | ( ( c_Objects_Otypeof__h @ D @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_1) ).

thf(1951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(1687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(136,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I118_J_0) ).

thf(1159,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(602,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).

thf(2327,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(609,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(2345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(596,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Map_Omap__comp @ E @ A @ B @ C @ F @ G )
        = ( hAPP @ E @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__simps_I2_J_0) ).

thf(2313,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Map_Omap__comp @ E @ A @ B @ C @ F @ G )
        = ( hAPP @ E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ooconf @ A @ B @ C @ D )
      | ~ ( c_Objects_Ohext @ E @ B )
      | ~ ( c_Conform_Ooconf @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_oconf__hext_0) ).

thf(1281,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ooconf @ A @ B @ C @ D )
      | ~ ( c_Objects_Ohext @ E @ B )
      | ~ ( c_Conform_Ooconf @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1634,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(648,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ D ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ ( hAPP @ A @ E ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apfst__conv_0) ).

thf(2433,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ D ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ ( hAPP @ A @ E ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(667,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ D @ H @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow2_0) ).

thf(2477,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ D @ H @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(709,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) )
      | ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of__zip__is__Some_1) ).

thf(2565,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) )
      | ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_snd @ A @ B @ C )
       != ( c_snd @ D @ B @ C ) )
      | ( ( c_fst @ A @ B @ C )
       != ( c_fst @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__fst__snd__eq_0) ).

thf(879,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_snd @ A @ B @ C )
       != ( c_snd @ D @ B @ C ) )
      | ( ( c_fst @ A @ B @ C )
       != ( c_fst @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(752,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_Map_Omap__comp @ D @ A @ B @ C @ E @ F )
        = ( c_Option_Ooption_ONone @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__simps_I1_J_0) ).

thf(2663,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_Map_Omap__comp @ D @ A @ B @ C @ E @ F )
        = ( c_Option_Ooption_ONone @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(604,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).

thf(2332,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(486,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallObjThrow_0) ).

thf(2068,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(1819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(547,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_Option_Ois__none @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__none__code_I2_J_0) ).

thf(2200,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_Option_Ois__none @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(728,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_Map_Oran @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ E @ C )
        = ( c_Set_Oinsert @ D @ ( c_Map_Oran @ A @ E @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ran__map__upd_0) ).

thf(2609,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_Map_Oran @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ E @ C )
        = ( c_Set_Oinsert @ D @ ( c_Map_Oran @ A @ E @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(383,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryReds_0) ).

thf(1836,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(538,axiom,
    ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
    = v_P ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(2181,plain,
    ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(1195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(551,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ D @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ D @ E @ C ) @ B )
        = ( c_Option_Ooption_ONone @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_2) ).

thf(2211,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ D @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ D @ E @ C ) @ B )
        = ( c_Option_Ooption_ONone @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(219,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).

thf(1407,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(506,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OBinOpThrow1_0) ).

thf(2112,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(179,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).

thf(1291,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(341,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oscomp @ A @ B @ t_a @ C @ D @ E ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_split @ C @ D @ E ) @ B ) @ ( hAPP @ A @ v_x ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scomp__def_0) ).

thf(1740,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oscomp @ A @ B @ t_a @ C @ D @ E ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_split @ C @ D @ E ) @ B ) @ ( hAPP @ A @ v_x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(414,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OThrowThrow_0) ).

thf(1910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(22,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).

thf(842,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(747,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ E )
      | ( ( hAPP @ C @ ( c_Conform_Osko__Conform__Xlconf__def__1__2 @ D @ A @ B @ C @ E ) )
        = ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ ( c_Conform_Osko__Conform__Xlconf__def__1__3 @ D @ A @ B @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lconf__def_2) ).

thf(2653,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ E )
      | ( ( hAPP @ C @ ( c_Conform_Osko__Conform__Xlconf__def__1__2 @ D @ A @ B @ C @ E ) )
        = ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ ( c_Conform_Osko__Conform__Xlconf__def__1__3 @ D @ A @ B @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(118,axiom,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OAddr @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I10_J_0) ).

thf(1106,plain,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OAddr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1360,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(590,axiom,
    ! [A: $i] :
      ( ( c_Option_Oset @ ( c_Option_Ooption_ONone @ A ) @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty__eq_1) ).

thf(2300,plain,
    ! [A: $i] :
      ( ( c_Option_Oset @ ( c_Option_Ooption_ONone @ A ) @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(508,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow1_0) ).

thf(2115,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(434,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      | ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

thf(1953,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      | ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ B @ A @ C @ D ) @ C @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).

thf(1064,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ B @ A @ C @ D ) @ C @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(281,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ F @ E ) @ G )
        = ( hAPP @ ( c_Fun_Ocomp @ ( c_Fun_Othe__inv__into @ A @ C @ F @ D ) @ ( c_Fun_Othe__inv__into @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ E ) @ D @ F @ E ) @ G ) )
      | ~ ( hBOOL @ ( c_in @ G @ ( c_Set_Oimage @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ C @ A @ F @ D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__comp_0) ).

thf(1587,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ F @ E ) @ G )
        = ( hAPP @ ( c_Fun_Ocomp @ ( c_Fun_Othe__inv__into @ A @ C @ F @ D ) @ ( c_Fun_Othe__inv__into @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ E ) @ D @ F @ E ) @ G ) )
      | ~ ( hBOOL @ ( c_in @ G @ ( c_Set_Oimage @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ C @ A @ F @ D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Set_Oimage @ C @ A @ F @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(226,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Oconf @ A @ B @ C @ D @ E )
      | ~ ( c_Conform_Oconf @ A @ F @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__hext_0) ).

thf(1425,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Oconf @ A @ B @ C @ D @ E )
      | ~ ( c_Conform_Oconf @ A @ F @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(683,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(2509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).

thf(1118,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(351,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsThrowObj_0) ).

thf(1762,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(686,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(2515,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(355,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccRedsThrow_0) ).

thf(1772,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(209,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I99_J_0) ).

thf(1375,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(123,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ E @ A @ C @ D ) @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).

thf(1121,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ E @ A @ C @ D ) @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(401,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).

thf(1878,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(738,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

thf(2631,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(129,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).

thf(1138,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(696,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ( hBOOL @ ( c_in @ E @ ( c_Map_Odom @ A @ C @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).

thf(2537,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ( hBOOL @ ( c_in @ E @ ( c_Map_Odom @ A @ C @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(659,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ~ ( c_Conform_Ooconf @ C @ A @ D @ E )
      | ( c_Conform_Ooconf @ C @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_oconf__new_0) ).

thf(2460,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ~ ( c_Conform_Ooconf @ C @ A @ D @ E )
      | ( c_Conform_Ooconf @ C @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(36,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).

thf(884,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(88,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I215_J_0) ).

thf(1028,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(204,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).

thf(1361,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(600,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__fun__upd_0) ).

thf(2323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(595,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow2_0) ).

thf(2312,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(564,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
      | ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) )
        = ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) ) )
        = ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_5) ).

thf(2240,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
      | ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) )
        = ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) ) )
        = ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(280,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).

thf(1584,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(426,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds_0) ).

thf(1937,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(155,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).

thf(1214,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(504,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(2108,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(753,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).

thf(2666,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(406,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ D @ ( c_fst @ E @ A @ B ) ) @ ( c_snd @ E @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__beta_0) ).

thf(1889,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ D @ ( c_fst @ E @ A @ B ) ) @ ( c_snd @ E @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(343,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
      | ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ A @ F @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).

thf(1744,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
      | ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ A @ F @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ B @ ( c_Fun_Oswap @ A @ B @ C @ D @ E ) @ D @ E )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_swap__nilpotent_0) ).

thf(901,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ B @ ( c_Fun_Oswap @ A @ B @ C @ D @ E ) @ D @ E )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(106,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1075,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(84,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_3) ).

thf(1016,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(494,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( c_State_Ohp @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ( c_SmallStep_Oredp @ H @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedFAcc_0) ).

thf(2085,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( c_State_Ohp @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ( c_SmallStep_Oredp @ H @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(745,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(2649,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I132_J_0) ).

thf(1039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(67,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).

thf(970,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(592,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsObj_0) ).

thf(2304,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ A @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).

thf(1831,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ A @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(681,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__cases_I1_J_1) ).

thf(2505,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(676,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I5_J_0) ).

thf(2497,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(431,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Throw_0) ).

thf(1947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(449,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).

thf(1984,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(399,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WhileCondThrow_0) ).

thf(1874,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(478,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_BigStep_Oeval @ C @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ E ) @ F @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__hext_0) ).

thf(2052,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_BigStep_Oeval @ C @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ E ) @ F @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(333,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_SmallStep_Oredp @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OThrowRed_0) ).

thf(1720,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_SmallStep_Oredp @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(577,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ B @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ D @ ( c_fst @ E @ A @ B ) ) @ ( c_snd @ E @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__case__beta_0) ).

thf(2272,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ B @ C ) @ D ) @ E )
      = ( hAPP @ ( hAPP @ D @ ( c_fst @ E @ A @ B ) ) @ ( c_snd @ E @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(519,axiom,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ B ) )
       != ( hAPP @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ H ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ J ) @ K ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ J @ L @ M @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ K ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ ( c_Fun_Ofun__upd @ B @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ L ) @ M ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ H ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsVal_0) ).

thf(2140,plain,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ B ) )
       != ( hAPP @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ H ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ J ) @ K ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ J @ L @ M @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ K ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ ( c_Fun_Ofun__upd @ B @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ L ) @ M ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ H ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(349,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OFAssThrow2_0) ).

thf(1759,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(620,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssRedsThrow_0) ).

thf(2370,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(378,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).

thf(1825,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(583,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) @ ( tc_prod @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(2285,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) @ ( tc_prod @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(680,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedTry_0) ).

thf(2504,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(72,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).

thf(985,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(133,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Option_Ooption_ONone @ B ) )
      | ~ ( hBOOL @ ( c_Option_Ois__none @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__none__def_0) ).

thf(1150,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Option_Ooption_ONone @ B ) )
      | ~ ( hBOOL @ ( c_Option_Ois__none @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Ointernal__split @ A @ B @ C )
      = ( c_split @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_internal__split__def_0) ).

thf(1478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Ointernal__split @ A @ B @ C )
      = ( c_split @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(760,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__empty_0) ).

thf(2681,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(263,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_Set_Oimage @ C @ D @ E @ F ) @ F @ A )
        = ( c_Finite__Set_Osetsum @ ( c_Fun_Ocomp @ B @ C @ F @ A @ E ) @ D @ E @ A ) )
      | ~ ( c_Fun_Oinj__on @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__reindex_0) ).

thf(1530,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_Set_Oimage @ C @ D @ E @ F ) @ F @ A )
        = ( c_Finite__Set_Osetsum @ ( c_Fun_Ocomp @ B @ C @ F @ A @ E ) @ D @ E @ A ) )
      | ~ ( c_Fun_Oinj__on @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(266,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).

thf(1539,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(211,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).

thf(1382,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(310,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).

thf(1668,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(445,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(1974,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(270,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).

thf(1552,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(565,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Conform_Ohconf @ E @ A @ F )
      | ( c_Conform_Ohconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ G ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ F )
      | ~ ( c_Conform_Ooconf @ E @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ G ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hconf__upd__obj_0) ).

thf(2243,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Conform_Ohconf @ E @ A @ F )
      | ( c_Conform_Ohconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ G ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ F )
      | ~ ( c_Conform_Ooconf @ E @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ G ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(614,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(2355,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I130_J_0) ).

thf(1192,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(424,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) )
       != ( hAPP @ C @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) ) )
      | ( ( c_Option_Ooption_Ooption__case @ F @ A @ B @ E @ D )
        = ( c_Option_Ooption_Ooption__case @ F @ C @ B @ E @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Ocase__cong_3) ).

thf(1932,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) )
       != ( hAPP @ C @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) ) )
      | ( ( c_Option_Ooption_Ooption__case @ F @ A @ B @ E @ D )
        = ( c_Option_Ooption_Ooption__case @ F @ C @ B @ E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OAddr @ A )
       != ( c_Value_Oval_OAddr @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I3_J_0) ).

thf(1060,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OAddr @ A )
       != ( c_Value_Oval_OAddr @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(96,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).

thf(1050,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(717,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).

thf(2581,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(661,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__out_0) ).

thf(2465,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I221_J_0) ).

thf(1002,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(389,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ( c_WellTypeRT_OWTrt @ D @ A @ E @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtVal_0) ).

thf(1852,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ( c_WellTypeRT_OWTrt @ D @ A @ E @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(447,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( hAPP @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ~ ( c_BigStep_Oeval @ H @ I @ J @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ K ) )
      | ( c_BigStep_Oeval @ H @ ( c_Expr_Oexp_OFAcc @ I @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ J @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAcc_0) ).

thf(1979,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( hAPP @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ~ ( c_BigStep_Oeval @ H @ I @ J @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ K ) )
      | ( c_BigStep_Oeval @ H @ ( c_Expr_Oexp_OFAcc @ I @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ J @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ K ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(1,negated_conjecture,
    ~ ( c_Conform_Olconf @ v_P @ ( c_Fun_Ofun__upd @ v_ha______ @ v_a______ @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ v_C______ ) @ ( c_Fun_Ofun__upd @ v_fs______ @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_F______ ) @ v_D______ ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ v_v______ ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ v_la______ @ v_E____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(779,plain,
    ~ ( c_Conform_Olconf @ v_P @ ( c_Fun_Ofun__upd @ v_ha______ @ v_a______ @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ v_C______ ) @ ( c_Fun_Ofun__upd @ v_fs______ @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_F______ ) @ v_D______ ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ v_v______ ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ v_la______ @ v_E____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(193,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I123_J_0) ).

thf(1333,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(150,axiom,
    ! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).

thf(1202,plain,
    ! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(321,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedBlock_0) ).

thf(1695,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(49,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).

thf(921,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(240,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).

thf(1466,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(555,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow1_0) ).

thf(2221,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(732,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(2617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(751,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ A @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedLAss_0) ).

thf(2662,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ A @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(644,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D )
      = ( hAPP @ ( c_Product__Type_Oprod__fun @ ( c_Fun_Oid @ C ) @ C @ C @ A @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__def_0) ).

thf(2423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D )
      = ( hAPP @ ( c_Product__Type_Oprod__fun @ ( c_Fun_Oid @ C ) @ C @ C @ A @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(51,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).

thf(926,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(229,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I200_J_0) ).

thf(1434,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_4) ).

thf(1857,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(373,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_Ooption__case @ A @ B @ C @ D @ E )
        = ( c_Option_Ooption_Ooption__case @ F @ G @ C @ D @ E ) )
      | ( C
        = ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ C @ B @ G @ E @ D ) ) )
      | ( C
        = ( c_Option_Ooption_ONone @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Ocase__cong_0) ).

thf(1814,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_Ooption__case @ A @ B @ C @ D @ E )
        = ( c_Option_Ooption_Ooption__case @ F @ G @ C @ D @ E ) )
      | ( C
        = ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ C @ B @ G @ E @ D ) ) )
      | ( C
        = ( c_Option_Ooption_ONone @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I49_J_0) ).

thf(938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(550,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(2208,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

thf(805,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(387,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ A @ B @ C ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ E ) )
      | ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ofilter @ ( hAPP @ ( c_split @ B @ C @ tc_bool ) @ F ) @ A @ ( tc_prod @ B @ C ) ) @ B @ C ) @ D )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of__filter__in_0) ).

thf(1846,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ A @ B @ C ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ E ) )
      | ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ofilter @ ( hAPP @ ( c_split @ B @ C @ tc_bool ) @ F ) @ A @ ( tc_prod @ B @ C ) ) @ B @ C ) @ D )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(98,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ B @ C @ D @ E )
      = ( c_Fun_Oswap @ B @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_swap__commute_0) ).

thf(1054,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ B @ C @ D @ E )
      = ( c_Fun_Oswap @ B @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(636,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OCond @ B @ ( c_Expr_Oexp_OSeq @ C @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedWhile_0) ).

thf(2408,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OCond @ B @ ( c_Expr_Oexp_OSeq @ C @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(308,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).

thf(1663,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(175,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( c_Set_Oimage @ C @ D @ E @ F ) @ F @ A )
        = ( c_Finite__Set_Osetprod @ ( c_Fun_Ocomp @ B @ C @ F @ A @ E ) @ D @ E @ A ) )
      | ~ ( c_Fun_Oinj__on @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__reindex_0) ).

thf(1278,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( c_Set_Oimage @ C @ D @ E @ F ) @ F @ A )
        = ( c_Finite__Set_Osetprod @ ( c_Fun_Ocomp @ B @ C @ F @ A @ E ) @ D @ E @ A ) )
      | ~ ( c_Fun_Oinj__on @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I73_J_0) ).

thf(1135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(456,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ( ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ ( hAPP @ A @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__eq_0) ).

thf(2001,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ( ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ ( hAPP @ A @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(352,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ ( c_Fun_Oid @ D ) @ F @ D @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ G ) )
        = ( hAPP @ F @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).

thf(1764,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ ( c_Fun_Oid @ D ) @ F @ D @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ G ) )
        = ( hAPP @ F @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(535,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastReds_0) ).

thf(2176,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(587,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) )
       != ( hAPP @ C @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) ) )
      | ( B
        = ( c_Option_Ooption_ONone @ D ) )
      | ( ( c_Option_Ooption_Ooption__case @ F @ A @ B @ E @ D )
        = ( c_Option_Ooption_Ooption__case @ G @ C @ B @ E @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Ocase__cong_1) ).

thf(2292,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) )
       != ( hAPP @ C @ ( c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1 @ B @ A @ C @ D @ E ) ) )
      | ( B
        = ( c_Option_Ooption_ONone @ D ) )
      | ( ( c_Option_Ooption_Ooption__case @ F @ A @ B @ E @ D )
        = ( c_Option_Ooption_Ooption__case @ G @ C @ B @ E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(629,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(2391,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(776,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OTryCatch @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OTryRed_0) ).

thf(2717,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OTryCatch @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Option_Oset @ A @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_elem__set_0) ).

thf(2028,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Option_Oset @ A @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(690,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OFAccThrow_0) ).

thf(2524,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(297,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I122_J_0) ).

thf(1631,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(511,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
      | ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).

thf(2121,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
      | ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(562,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(2235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(44,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).

thf(906,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(438,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1959,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(705,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OCastThrow_0) ).

thf(2556,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(570,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).

thf(2253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(523,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_snd @ ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ E ) @ C @ D )
      = ( c_snd @ E @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__apfst_0) ).

thf(2149,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_snd @ ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ E ) @ C @ D )
      = ( c_snd @ E @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(15,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).

thf(819,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(417,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).

thf(1916,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(476,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__fun__upd_0) ).

thf(2048,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(557,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedInitBlock_0) ).

thf(2225,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(691,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OLAssThrow_0) ).

thf(2525,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(672,axiom,
    c_Conform_Olconf @ v_P @ v_ha______ @ v_la______ @ v_E____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(2489,plain,
    c_Conform_Olconf @ v_P @ v_ha______ @ v_la______ @ v_E____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(213,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).

thf(1388,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(17,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I208_J_0) ).

thf(826,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

thf(958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(324,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_curry @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curry__conv_0) ).

thf(1701,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_curry @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).

thf(1615,plain,
    ! [B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(360,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(1784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
        = ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).

thf(1652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
        = ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit__asm_4) ).

thf(1929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(757,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_5) ).

thf(2674,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(710,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OThrowThrow_0) ).

thf(2568,plain,
    ! [C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(767,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Conform_Osko__Conform__Xlconf__def__1__2 @ A @ B @ C @ D @ E ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ F ) )
      | ( c_Conform_Olconf @ B @ C @ D @ A @ E )
      | ~ ( c_Conform_Oconf @ B @ C @ ( c_Conform_Osko__Conform__Xlconf__def__1__3 @ A @ B @ C @ D @ E ) @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lconf__def_3) ).

thf(2695,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Conform_Osko__Conform__Xlconf__def__1__2 @ A @ B @ C @ D @ E ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ F ) )
      | ( c_Conform_Olconf @ B @ C @ D @ A @ E )
      | ~ ( c_Conform_Oconf @ B @ C @ ( c_Conform_Osko__Conform__Xlconf__def__1__3 @ A @ B @ C @ D @ E ) @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(1226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(395,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ E @ ( tc_prod @ A @ B ) ) @ A @ B ) @ F )
        = ( hAPP @ ( c_Map_Omap__of @ E @ A @ B ) @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of__Cons__code_I2_J_1) ).

thf(1865,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ E @ ( tc_prod @ A @ B ) ) @ A @ B ) @ F )
        = ( hAPP @ ( c_Map_Omap__of @ E @ A @ B ) @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(338,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCond @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OCondRed_0) ).

thf(1733,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCond @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(454,axiom,
    ( ( hAPP @ v_ha______ @ v_a______ )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ v_C______ ) @ v_fs______ ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(1997,plain,
    ( ( hAPP @ v_ha______ @ v_a______ )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ v_C______ ) @ v_fs______ ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

thf(1092,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(772,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).

thf(2706,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(645,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__rec @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Orecs_I2_J_0) ).

thf(2425,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__rec @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(665,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OBinOpThrow2_0) ).

thf(2474,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ ( c_Option_Ooption_ONone @ B ) )
      = ( c_Option_Ooption_ONone @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__None_0) ).

thf(2193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ ( c_Option_Ooption_ONone @ B ) )
      = ( c_Option_Ooption_ONone @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit__asm_5) ).

thf(1786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(531,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) @ ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exI__realizer_0) ).

thf(2166,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) @ ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(111,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__trans_0) ).

thf(1090,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(658,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ F @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ F @ E @ C ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).

thf(2457,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ F @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ F @ E @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(409,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ B @ D ) @ G ) )
      = ( hAPP @ ( c_Product__Type_Oapfst @ ( c_Fun_Ocomp @ A @ E @ B @ C @ F ) @ F @ C @ D ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apfst__compose_0) ).

thf(1897,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ B @ D ) @ G ) )
      = ( hAPP @ ( c_Product__Type_Oapfst @ ( c_Fun_Ocomp @ A @ E @ B @ C @ F ) @ F @ C @ D ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(713,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds2_0) ).

thf(2573,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(522,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBlockThrow_0) ).

thf(2148,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(70,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I159_J_0) ).

thf(979,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(688,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowRedsThrow_0) ).

thf(2521,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(3,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_0) ).

thf(784,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(82,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I190_J_0) ).

thf(1011,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(261,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).

thf(1524,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ C )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I4_J_0) ).

thf(1048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(77,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I100_J_0) ).

thf(996,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(367,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds1_0) ).

thf(1801,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ F ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(485,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) )
      | ~ ( c_Conform_Ohconf @ D @ A @ E )
      | ( c_Conform_Ooconf @ D @ A @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hconfD_0) ).

thf(2065,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) )
      | ~ ( c_Conform_Ohconf @ D @ A @ E )
      | ( c_Conform_Ooconf @ D @ A @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(153,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(1209,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(510,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ C @ A ) @ G ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ B ) @ ( hAPP @ E @ ( c_fst @ G @ F @ A ) ) ) @ ( hAPP @ D @ ( c_snd @ G @ F @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__apfst_0) ).

thf(2119,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ ( hAPP @ ( c_Product__Type_Oapfst @ E @ F @ C @ A ) @ G ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ B ) @ ( hAPP @ E @ ( c_fst @ G @ F @ A ) ) ) @ ( hAPP @ D @ ( c_snd @ G @ F @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(524,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Objects_Ohext @ A @ E )
      | ( ( hAPP @ E @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Objects_Osko__Objects__Xhext__objD__1__1 @ C @ B @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__objD_0) ).

thf(2151,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Objects_Ohext @ A @ E )
      | ( ( hAPP @ E @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Objects_Osko__Objects__Xhext__objD__1__1 @ C @ B @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(559,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(2229,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
      = ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).

thf(2214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
      = ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(625,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
        = ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ D @ E ) @ D ) )
      | ( C
        = ( c_Option_Ooption_ONone @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).

thf(2383,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
        = ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ D @ E ) @ D ) )
      | ( C
        = ( c_Option_Ooption_ONone @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(735,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow1_0) ).

thf(2624,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ D @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domIff_0) ).

thf(1894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ D @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(674,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ t_b @ t_c @ t_a ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Pair @ t_b @ t_c ) @ C ) @ D ) ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod_Osplit__asm_0) ).

thf(2493,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ t_b @ t_c @ t_a ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Pair @ t_b @ t_c ) @ C ) @ D ) ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(199,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Othrow @ A @ B )
       != ( c_Expr_Oexp_Othrow @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).

thf(1349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Othrow @ A @ B )
       != ( c_Expr_Oexp_Othrow @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(499,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp1Reds_0) ).

thf(2097,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(566,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OCondThrow_0) ).

thf(2246,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(287,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).

thf(1603,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(131,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).

thf(1144,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(623,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Othe @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the_Osimps_0) ).

thf(2378,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Othe @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(1690,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( c_SmallStep_Ored @ C ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).

thf(2197,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ B ) ) @ ( c_SmallStep_Ored @ C ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(442,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OBinOp @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OBinOpRed1_0) ).

thf(1969,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OBinOp @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(184,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I110_J_0) ).

thf(1307,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVar @ A @ B )
       != ( c_Expr_Oexp_OVar @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I5_J_0) ).

thf(1080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVar @ A @ B )
       != ( c_Expr_Oexp_OVar @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(27,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).

thf(858,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(514,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oscomp @ A @ B @ C @ D @ E @ F ) @ G )
      = ( hAPP @ ( hAPP @ ( c_split @ D @ E @ F ) @ B ) @ ( hAPP @ A @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scomp__apply_0) ).

thf(2129,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oscomp @ A @ B @ C @ D @ E @ F ) @ G )
      = ( hAPP @ ( hAPP @ ( c_split @ D @ E @ F ) @ B ) @ ( hAPP @ A @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I117_J_0) ).

thf(816,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(376,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow2_0) ).

thf(1821,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(654,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).

thf(2446,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(393,axiom,
    ! [A: $i] :
      ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Fun_Oid @ A ) @ A @ A )
      = ( c_Fun_Oid @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__id_0) ).

thf(1862,plain,
    ! [A: $i] :
      ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Fun_Oid @ A ) @ A @ A )
      = ( c_Fun_Oid @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(384,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ B ) )
      | ( ( c_Map_Omap__comp @ A @ E @ F @ G @ C @ H )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__Some__iff_2) ).

thf(1838,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ B ) )
      | ( ( c_Map_Omap__comp @ A @ E @ F @ G @ C @ H )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(40,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).

thf(895,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(65,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I134_J_0) ).

thf(964,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_2) ).

thf(915,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(86,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

thf(1022,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(580,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondRedsThrow_0) ).

thf(2278,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(142,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).

thf(1177,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(38,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I178_J_0) ).

thf(890,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(537,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).

thf(2180,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(8,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).

thf(799,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(137,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).

thf(1162,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(271,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I205_J_0) ).

thf(1556,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(698,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

thf(2542,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(238,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).

thf(1460,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(603,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ A @ B @ C )
       != ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A
        = ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1 @ A @ D @ B @ C ) ) @ B @ ( tc_Option_Ooption @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_0) ).

thf(2329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ A @ B @ C )
       != ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A
        = ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1 @ A @ D @ B @ C ) ) @ B @ ( tc_Option_Ooption @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(53,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I214_J_0) ).

thf(932,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(120,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).

thf(1112,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(716,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
       != ( c_Fun_Oid @ A ) )
      | ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__iff_1) ).

thf(2578,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
       != ( c_Fun_Oid @ A ) )
      | ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(641,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OLAss @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OLAssRed_0) ).

thf(2418,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OLAss @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(611,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ ( c_Expr_Oexp_OSeq @ C @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unfold__while_1) ).

thf(2350,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ ( c_Expr_Oexp_OSeq @ C @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(533,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Otop @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(2171,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Otop @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).

thf(1066,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(585,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ G @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Seq_0) ).

thf(2288,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ G @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(721,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ H ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ H ) ) ) @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedFAss_0) ).

thf(2592,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ H ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ H ) ) ) @ ( c_SmallStep_Ored @ I ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(205,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).

thf(1364,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(526,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Product__Type_Oapfst @ F @ B @ C @ D ) @ E ) )
      | ( ( hAPP @ A @ ( c_fst @ E @ B @ D ) )
        = ( hAPP @ F @ ( c_fst @ E @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apfst__eq__conv_0) ).

thf(2156,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Product__Type_Oapfst @ F @ B @ C @ D ) @ E ) )
      | ( ( hAPP @ A @ ( c_fst @ E @ B @ D ) )
        = ( hAPP @ F @ ( c_fst @ E @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(766,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod_Ocases_0) ).

thf(2693,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(273,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I165_J_0) ).

thf(1562,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(46,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I142_J_0) ).

thf(912,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(140,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I112_J_0) ).

thf(1171,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(149,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).

thf(1198,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(385,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ B ) @ v_x )
      = ( c_Option_Ooption_ONone @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).

thf(1841,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ B ) @ v_x )
      = ( c_Option_Ooption_ONone @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(323,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_split @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ F ) @ G ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ E @ F ) @ G ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__splitI_0) ).

thf(1699,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_split @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ F ) @ G ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ E @ F ) @ G ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(633,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ohconf @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Conform_Ohconf @ A @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ E @ F )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ H ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ I ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__preserves__hconf_0) ).

thf(2401,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ohconf @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Conform_Ohconf @ A @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ E @ F )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ H ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ I ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).

thf(1594,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(477,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).

thf(2051,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(701,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ D ) )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__Some_0) ).

thf(2550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ D ) )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(165,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(669,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ( c_WellTypeRT_OWTrt @ D @ E @ A @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtVar_0) ).

thf(2481,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ( c_WellTypeRT_OWTrt @ D @ E @ A @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(739,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Exceptions_Opreallocated @ A )
      | ( c_Exceptions_Opreallocated @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ E ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_preallocated__upd__obj_0) ).

thf(2633,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Exceptions_Opreallocated @ A )
      | ( c_Exceptions_Opreallocated @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ E ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(464,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ ( c_Map_Odom @ B @ C @ D ) @ C @ ( tc_Option_Ooption @ D ) )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Map_Odom @ B @ C @ D ) @ C @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__map__add__dom_1) ).

thf(2022,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ ( c_Map_Odom @ B @ C @ D ) @ C @ ( tc_Option_Ooption @ D ) )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Map_Odom @ B @ C @ D ) @ C @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(695,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(2535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(501,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

thf(2101,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(25,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).

thf(851,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(116,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Oswap @ B @ C @ D @ E @ F ) @ F @ G @ E )
      = ( c_Fun_Oswap @ B @ C @ ( c_Fun_Ocomp @ A @ D @ F @ G @ E ) @ E @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__swap_0) ).

thf(1102,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Oswap @ B @ C @ D @ E @ F ) @ F @ G @ E )
      = ( c_Fun_Oswap @ B @ C @ ( c_Fun_Ocomp @ A @ D @ F @ G @ E ) @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OSeqThrow_0) ).

thf(1973,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(1805,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(479,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_COMBK @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ ( tc_Option_Ooption @ A ) @ C ) @ C @ A )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__const_0) ).

thf(2054,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_COMBK @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ ( tc_Option_Ooption @ A ) @ C ) @ C @ A )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(90,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I111_J_0) ).

thf(1034,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(371,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).

thf(1809,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(730,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ ( c_Expr_Oexp_OSeq @ B @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedWhile_0) ).

thf(2614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ ( c_Expr_Oexp_OSeq @ B @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1203,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(57,axiom,
    ! [A: $i] : ( hBOOL @ ( c_Option_Ois__none @ ( c_Option_Ooption_ONone @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__none__def_1) ).

thf(944,plain,
    ! [A: $i] : ( hBOOL @ ( c_Option_Ois__none @ ( c_Option_Ooption_ONone @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(598,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( c_Conform_Olconf @ D @ E @ A @ F @ G )
      | ( c_Conform_Oconf @ D @ E @ C @ ( c_Conform_Osko__Conform__Xlconf__def__1__1 @ F @ D @ B @ E @ C @ G ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lconf__def_1) ).

thf(2318,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( c_Conform_Olconf @ D @ E @ A @ F @ G )
      | ( c_Conform_Oconf @ D @ E @ C @ ( c_Conform_Osko__Conform__Xlconf__def__1__1 @ F @ D @ B @ E @ C @ G ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(224,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I148_J_0) ).

thf(1420,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(471,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(2037,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ ( c_fst @ C @ A @ B ) ) @ ( c_snd @ C @ A @ B ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__collapse_0) ).

thf(1684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ ( c_fst @ C @ A @ B ) ) @ ( c_snd @ C @ A @ B ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(512,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
       != A )
      | ( ( hAPP @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(2124,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
       != A )
      | ( ( hAPP @ A @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(255,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I94_J_0) ).

thf(1509,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(737,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).

thf(2629,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(242,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I172_J_0) ).

thf(1472,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(20,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I105_J_0) ).

thf(836,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(183,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).

thf(1304,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(398,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ A @ D @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__None__map__le_0) ).

thf(1873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ A @ D @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(451,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ F @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_1) ).

thf(1990,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ F @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(762,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ t_b @ t_c @ t_a ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Pair @ t_b @ t_c ) @ C ) @ D ) ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod_Osplit_0) ).

thf(2684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ t_b @ t_c @ t_a ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Pair @ t_b @ t_c ) @ C ) @ D ) ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(548,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ A @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_1) ).

thf(2202,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ A @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(85,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).

thf(1018,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(571,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ( hBOOL @ ( c_in @ E @ ( c_Map_Odom @ B @ C @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).

thf(2256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ( hBOOL @ ( c_in @ E @ ( c_Map_Odom @ B @ C @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(685,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_snd @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ E ) @ C @ B )
      = ( hAPP @ D @ ( c_snd @ E @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__apsnd_0) ).

thf(2513,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_snd @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ E ) @ C @ B )
      = ( hAPP @ D @ ( c_snd @ E @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(345,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(1748,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(26,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I196_J_0) ).

thf(855,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(87,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).

thf(1025,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(37,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I129_J_0) ).

thf(887,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(1780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(1098,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ~ ( c_Exceptions_Opreallocated @ A )
      | ( c_Exceptions_Opreallocated @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_preallocated__new_0) ).

thf(1798,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ~ ( c_Exceptions_Opreallocated @ A )
      | ( c_Exceptions_Opreallocated @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(589,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryRedsVal_0) ).

thf(2298,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(290,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).

thf(1611,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(622,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ A @ C @ D ) @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).

thf(2375,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ A @ C @ D ) @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(135,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).

thf(1156,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(482,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).

thf(2060,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(1400,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(520,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__restrict_0) ).

thf(2143,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(460,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ E @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ E @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__minus_0) ).

thf(2012,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ E @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ E @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(428,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_curry @ A @ B @ C @ tc_bool ) @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curryD_0) ).

thf(1941,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_curry @ A @ B @ C @ tc_bool ) @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).

thf(1252,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(759,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( c_State_Ohp @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedFAcc_0) ).

thf(2678,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) )
      | ( ( c_State_Ohp @ E @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G ) @ A ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(687,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ E )
       != ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ F ) @ E ) )
      | ( ( hAPP @ D @ ( c_snd @ E @ C @ A ) )
        = ( hAPP @ F @ ( c_snd @ E @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__eq__conv_0) ).

thf(2518,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ D ) @ E )
       != ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ A @ B @ C ) @ F ) @ E ) )
      | ( ( hAPP @ D @ ( c_snd @ E @ C @ A ) )
        = ( hAPP @ F @ ( c_snd @ E @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(347,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_0) ).

thf(1753,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(626,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__comp @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ v_x @ B @ A @ t_a )
      = ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__empty_I2_J_0) ).

thf(2386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__comp @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ v_x @ B @ A @ t_a )
      = ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(711,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ooverride__on @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__emptyset_0) ).

thf(2569,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ooverride__on @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(497,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).

thf(2092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(530,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow1_0) ).

thf(2165,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(606,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).

thf(2337,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(474,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(2044,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(278,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).

thf(1579,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(194,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(1336,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(748,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__f_0) ).

thf(2656,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(329,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
        = ( c_Set_Oimage @ A @ F @ D @ E ) )
      | ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

thf(1711,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
        = ( c_Set_Oimage @ A @ F @ D @ E ) )
      | ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(363,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ D )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( D
        = ( c_Option_Ooption_ONone @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__is__None_0) ).

thf(1790,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ D )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( D
        = ( c_Option_Ooption_ONone @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(450,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ D @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ B ) )
      | ( ( c_Map_Omap__comp @ A @ D @ E @ F @ C @ G )
        = ( c_Option_Ooption_ONone @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__None__iff_3) ).

thf(1987,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ D @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ B ) )
      | ( ( c_Map_Omap__comp @ A @ D @ E @ F @ C @ G )
        = ( c_Option_Ooption_ONone @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(331,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).

thf(1716,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(657,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

thf(2454,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(182,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).

thf(1300,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(235,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVar @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I135_J_0) ).

thf(1452,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVar @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(764,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
      = ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ F ) @ A ) @ D ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zip__Cons__Cons_0) ).

thf(2688,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
      = ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ F ) @ A ) @ D ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(769,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).

thf(2700,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
        = E )
      | ~ ( hBOOL @ ( c_in @ E @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(145,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).

thf(1186,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(170,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I115_J_0) ).

thf(1262,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(162,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).

thf(1235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(579,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Orestrict__map @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ C @ D @ E ) @ B @ ( hAPP @ A @ B ) @ D @ ( tc_Option_Ooption @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__map__insert_0) ).

thf(2276,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Orestrict__map @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ C @ D @ E ) @ B @ ( hAPP @ A @ B ) @ D @ ( tc_Option_Ooption @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(554,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).

thf(2219,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(671,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_1) ).

thf(2486,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(699,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ A @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__cases_I1_J_0) ).

thf(2545,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(724,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(2599,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(662,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
      = ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(2468,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
      = ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(157,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).

thf(1220,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(678,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ A ) @ D ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__eqD_0) ).

thf(2500,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ A ) @ D ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(267,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I89_J_0) ).

thf(1543,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(388,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_snd @ B @ C @ D ) )
       != ( hAPP @ E @ ( c_snd @ B @ C @ D ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ D @ F @ C ) @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ D @ F @ C ) @ E ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__eq__conv_1) ).

thf(1849,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_snd @ B @ C @ D ) )
       != ( hAPP @ E @ ( c_snd @ B @ C @ D ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ D @ F @ C ) @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ D @ F @ C ) @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(29,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).

thf(864,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(227,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I124_J_0) ).

thf(1427,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).

thf(1504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(684,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBI @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(2511,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBI @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(332,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_Conform_Oconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ F ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ G @ H @ I )
      | ~ ( c_Conform_Oconf @ E @ A @ G @ H @ I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__upd__obj_1) ).

thf(1717,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ( c_Conform_Oconf @ E @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ F ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ G @ H @ I )
      | ~ ( c_Conform_Oconf @ E @ A @ G @ H @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(208,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).

thf(1372,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(173,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).

thf(1272,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(718,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).

thf(2584,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(480,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OCastRed_0) ).

thf(2056,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(218,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).

thf(1404,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(567,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(2247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(706,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OCondThrow_0) ).

thf(2558,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(507,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

thf(2113,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(130,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).

thf(1141,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(265,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I97_J_0) ).

thf(1536,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(200,axiom,
    class_Orderings_Otop @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(1353,plain,
    class_Orderings_Otop @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(615,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_0) ).

thf(2357,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(435,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).

thf(1955,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(521,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit__asm_3) ).

thf(2145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__asm__1 @ A @ C @ D ) ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(247,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).

thf(1485,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(97,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_1) ).

thf(1052,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(774,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Map_Odom @ B @ C @ D ) @ C ) )
      | ( ( hAPP @ B @ A )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domIff_1) ).

thf(2711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Map_Odom @ B @ C @ D ) @ C ) )
      | ( ( hAPP @ B @ A )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(778,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      = ( c_Map_Omap__upds @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ E ) @ D @ ( tc_Option_Ooption @ G ) ) @ C @ F @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Cons_0) ).

thf(2722,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      = ( c_Map_Omap__upds @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ E ) @ D @ ( tc_Option_Ooption @ G ) ) @ C @ F @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(81,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).

thf(1008,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(575,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ( c_BigStep_Oeval @ D @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ A ) @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_0) ).

thf(2266,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ( c_BigStep_Oeval @ D @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ A ) @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(33,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).

thf(876,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(74,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(991,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(292,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

thf(1617,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(649,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(2435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(668,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ ( c_Fun_Ocomp @ D @ E @ F @ ( tc_fun @ B @ C ) @ A ) ) @ G )
      = ( hAPP @ ( hAPP @ D @ ( hAPP @ E @ ( c_fst @ G @ A @ B ) ) ) @ ( c_snd @ G @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__comp_0) ).

thf(2479,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_split @ A @ B @ C ) @ ( c_Fun_Ocomp @ D @ E @ F @ ( tc_fun @ B @ C ) @ A ) ) @ G )
      = ( hAPP @ ( hAPP @ D @ ( hAPP @ E @ ( c_fst @ G @ A @ B ) ) ) @ ( c_snd @ G @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(495,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__map__add_0) ).

thf(2088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_Finite__Set_Osetsum @ ( c_Fun_Oid @ A ) @ ( c_Set_Oimage @ B @ C @ D @ A ) @ A @ A ) )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__reindex__id_0) ).

thf(1180,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_Finite__Set_Osetsum @ ( c_Fun_Oid @ A ) @ ( c_Set_Oimage @ B @ C @ D @ A ) @ A @ A ) )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(441,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ( c_Conform_Oconf @ D @ A @ B @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typeof__conf_0) ).

thf(1966,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ C ) )
      | ( c_Conform_Oconf @ D @ A @ B @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(432,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1949,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(374,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ D @ E @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OBinOpRed2_0) ).

thf(1817,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ D @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(258,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1517,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(601,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__All__1__1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__paired__All_0) ).

thf(2325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__All__1__1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(125,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I209_J_0) ).

thf(1126,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(488,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).

thf(2071,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(370,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_fst @ ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ E ) @ C @ D )
      = ( hAPP @ A @ ( c_fst @ E @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__apfst_0) ).

thf(1807,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_fst @ ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ E ) @ C @ D )
      = ( hAPP @ A @ ( c_fst @ E @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(736,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ( c_Objects_Ohext @ A @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__new_0) ).

thf(2626,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ( c_Objects_Ohext @ A @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(418,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ ( c_Expr_Oexp_OSeq @ C @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unfold__while_0) ).

thf(1918,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ ( c_Expr_Oexp_OSeq @ C @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(187,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).

thf(1316,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(303,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I179_J_0) ).

thf(1649,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(612,axiom,
    c_Conform_Olconf @ v_P @ v_ha______ @ v_la______ @ v_E____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RedFAss_I3_J_0) ).

thf(2352,plain,
    c_Conform_Olconf @ v_P @ v_ha______ @ v_la______ @ v_E____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(109,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).

thf(1084,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(491,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ E @ C ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domI_0) ).

thf(2078,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ E @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oscomp @ A @ ( c_Pair @ B @ C ) @ D @ B @ C @ ( tc_prod @ B @ C ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scomp__Pair_0) ).

thf(1834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oscomp @ A @ ( c_Pair @ B @ C ) @ D @ B @ C @ ( tc_prod @ B @ C ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(69,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I65_J_0) ).

thf(976,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(43,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I46_J_0) ).

thf(903,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(673,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Objects_Ohext @ A @ E )
      | ( ( hAPP @ E @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Objects_Osko__Objects__Xhext__def__1__1 @ C @ B @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__def_0) ).

thf(2490,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_Objects_Ohext @ A @ E )
      | ( ( hAPP @ E @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Objects_Osko__Objects__Xhext__def__1__1 @ C @ B @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(541,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).

thf(2187,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

thf(1189,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(505,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ C ) @ C @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__empty_0) ).

thf(2110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ C ) @ C @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(608,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_Map_Omap__comp @ D @ A @ B @ C @ E @ F )
        = ( c_Option_Ooption_ONone @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__None__iff_2) ).

thf(2342,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_Map_Omap__comp @ D @ A @ B @ C @ E @ F )
        = ( c_Option_Ooption_ONone @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(277,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).

thf(1575,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(558,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( c_SmallStep_Oredp @ D @ E @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ ( c_Fun_Ofun__upd @ G @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ H ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ I @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ J ) @ A ) )
      | ( c_SmallStep_Oredp @ D @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ G ) @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ J ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ G @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OInitBlockRed_0) ).

thf(2226,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ~ ( c_SmallStep_Oredp @ D @ E @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ ( c_Fun_Ofun__upd @ G @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ H ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ I @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ J ) @ A ) )
      | ( c_SmallStep_Oredp @ D @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ G ) @ ( c_Expr_Oexp_OBlock @ B @ K @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ J ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ G @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(743,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Ofilter @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).

thf(2643,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Ofilter @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1590,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(191,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).

thf(1326,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(628,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ E @ D @ B ) @ F ) @ G ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ ( hAPP @ A @ ( c_fst @ G @ B @ E ) ) ) @ ( hAPP @ F @ ( c_snd @ G @ B @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apfst__apsnd_0) ).

thf(2389,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oapsnd @ E @ D @ B ) @ F ) @ G ) )
      = ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ ( hAPP @ A @ ( c_fst @ G @ B @ E ) ) ) @ ( hAPP @ F @ ( c_snd @ G @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(196,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I125_J_0) ).

thf(1341,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVar @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(703,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) @ ( tc_prod @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(2554,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) @ ( tc_prod @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(457,axiom,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_BigStep_Oeval @ E @ F @ G @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ I ) )
      | ~ ( c_BigStep_Oeval @ E @ J @ K @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ( c_BigStep_Oeval @ E @ ( c_Expr_Oexp_OFAss @ J @ L @ M @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ K @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ L ) @ M ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ H ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ I ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAss_0) ).

thf(2004,plain,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) ) )
      | ~ ( c_BigStep_Oeval @ E @ F @ G @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ A ) @ I ) )
      | ~ ( c_BigStep_Oeval @ E @ J @ K @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ( c_BigStep_Oeval @ E @ ( c_Expr_Oexp_OFAss @ J @ L @ M @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ K @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ L ) @ M ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ H ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ I ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Option__Xospec__1__1 @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ C @ A ) @ ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A ) @ A ) )
      | ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ospec_0) ).

thf(2026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Option__Xospec__1__1 @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ C @ A ) @ ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A ) @ A ) )
      | ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(2,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).

thf(781,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(640,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ A @ B )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__conv_0) ).

thf(2416,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) @ A @ B )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(573,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ t_a @ A ) @ v_x )
      = ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__map__empty_0) ).

thf(2262,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ t_a @ A ) @ v_x )
      = ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(630,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed1_0) ).

thf(2394,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(64,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I222_J_0) ).

thf(961,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(13,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I120_J_0) ).

thf(813,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).

thf(1385,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(312,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(1674,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(300,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).

thf(1639,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(586,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).

thf(2290,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(569,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ F ) )
      | ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OLAss @ G @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ ( c_Fun_Ofun__upd @ F @ G @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAss_0) ).

thf(2251,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ F ) )
      | ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OLAss @ G @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E ) @ ( c_Fun_Ofun__upd @ F @ G @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(517,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ooconf @ A @ B @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ H )
      | ~ ( c_Conform_Ooconf @ A @ B @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) @ H )
      | ~ ( c_Conform_Oconf @ A @ B @ G @ I @ H )
      | ~ ( c_TypeRel_Ohas__field @ A @ C @ E @ I @ F @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_oconf__fupd_0) ).

thf(2135,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Ooconf @ A @ B @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ ( c_Fun_Ofun__upd @ D @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ G ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ H )
      | ~ ( c_Conform_Ooconf @ A @ B @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ C ) @ D ) @ H )
      | ~ ( c_Conform_Oconf @ A @ B @ G @ I @ H )
      | ~ ( c_TypeRel_Ohas__field @ A @ C @ E @ I @ F @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(635,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(2406,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(459,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__comp @ A @ B @ C @ D @ E @ F )
       != ( c_Option_Ooption_ONone @ E ) )
      | ( ( hAPP @ A @ ( c_Map_Osko__Map__Xmap__comp__None__iff__1__1 @ C @ A @ B @ F @ D @ E ) )
        = ( c_Option_Ooption_ONone @ E ) )
      | ( ( hAPP @ B @ C )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__None__iff_1) ).

thf(2009,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__comp @ A @ B @ C @ D @ E @ F )
       != ( c_Option_Ooption_ONone @ E ) )
      | ( ( hAPP @ A @ ( c_Map_Osko__Map__Xmap__comp__None__iff__1__1 @ C @ A @ B @ F @ D @ E ) )
        = ( c_Option_Ooption_ONone @ E ) )
      | ( ( hAPP @ B @ C )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(249,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I126_J_0) ).

thf(1491,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVar @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(492,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Try_0) ).

thf(2081,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(666,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(2475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(357,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

thf(1777,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(180,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I108_J_0) ).

thf(1294,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(52,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).

thf(929,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(546,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Ointernal__split @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_internal__split__conv_0) ).

thf(2198,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Product__Type_Ointernal__split @ A @ B @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
      = ( hAPP @ ( hAPP @ D @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(715,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccReds_0) ).

thf(2576,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(326,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondReds_0) ).

thf(1706,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(539,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(2183,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(307,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      = ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).

thf(1661,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      = ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(498,axiom,
    ( ( hAPP @ v_ha______ @ v_a______ )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ v_C______ ) @ v_fs______ ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RedFAss_Ohyps_0) ).

thf(2095,plain,
    ( ( hAPP @ v_ha______ @ v_a______ )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ v_C______ ) @ v_fs______ ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(560,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Othe__inv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).

thf(2230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Othe__inv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
        = D )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(232,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).

thf(1444,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(453,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).

thf(1994,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(94,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I137_J_0) ).

thf(1045,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(643,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ B @ C @ D @ E )
      = ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ C @ A @ ( hAPP @ C @ B ) @ D @ E ) @ B @ ( hAPP @ C @ A ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_swap__def_0) ).

thf(2421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oswap @ A @ B @ C @ D @ E )
      = ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ C @ A @ ( hAPP @ C @ B ) @ D @ E ) @ B @ ( hAPP @ C @ A ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(632,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_curry @ A @ B @ C @ tc_bool ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curryI_0) ).

thf(2399,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_curry @ A @ B @ C @ tc_bool ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(473,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).

thf(2041,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(107,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I64_J_0) ).

thf(1077,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(528,axiom,
    class_Orderings_Obot @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(2162,plain,
    class_Orderings_Obot @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I48_J_0) ).

thf(999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).

thf(1642,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(591,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WhileRedsThrow_0) ).

thf(2302,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(335,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
       != ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
      | ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
       != ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
      | ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_7) ).

thf(1725,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
       != ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
      | ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
       != ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
      | ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(437,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ ( c_Fun_Ofun__upd @ E @ A @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ E ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssRedsVal_0) ).

thf(1957,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ ( c_Fun_Ofun__upd @ E @ A @ ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ F ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ D ) @ E ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(314,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).

thf(1678,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(719,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Option_Oset_Osimps_I2_J_0) ).

thf(2587,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(268,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).

thf(1546,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(400,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__of @ ( c_List_Olist_OCons @ A @ B @ ( tc_prod @ C @ D ) ) @ C @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__of @ B @ C @ D ) @ ( c_fst @ A @ C @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ ( c_snd @ A @ C @ D ) ) @ C @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of_Osimps_I2_J_0) ).

thf(1876,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__of @ ( c_List_Olist_OCons @ A @ B @ ( tc_prod @ C @ D ) ) @ C @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__of @ B @ C @ D ) @ ( c_fst @ A @ C @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ ( c_snd @ A @ C @ D ) ) @ C @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(262,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I199_J_0) ).

thf(1527,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(30,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).

thf(867,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(245,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Oswap @ A @ B @ C @ D @ E ) @ F @ D @ E )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ F @ D ) )
      | ~ ( c_Fun_Oinj__on @ C @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imp__inj__on__swap_0) ).

thf(1480,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Oswap @ A @ B @ C @ D @ E ) @ F @ D @ E )
      | ~ ( hBOOL @ ( c_in @ B @ F @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ F @ D ) )
      | ~ ( c_Fun_Oinj__on @ C @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Exceptions_Opreallocated @ A )
      | ~ ( c_Conform_Ohconf @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hconf__def_1) ).

thf(1512,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Exceptions_Opreallocated @ A )
      | ~ ( c_Conform_Ohconf @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(356,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( D = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).

thf(1774,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( D = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).

thf(833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(66,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).

thf(967,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(777,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_State_Olcl @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ( c_SmallStep_Oredp @ D @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_ORedVar_0) ).

thf(2719,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_State_Olcl @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ tc_Value_Oval ) @ C ) )
      | ( c_SmallStep_Oredp @ D @ ( c_Expr_Oexp_OVar @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).

thf(1229,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(561,axiom,
    ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
    = v_x ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).

thf(2233,plain,
    ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
    = v_x ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I131_J_0) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVar @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(295,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).

thf(1625,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(166,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

thf(1248,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OVar @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I72_J_0) ).

thf(790,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OVar @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(740,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_fst @ B @ C @ D ) )
       != ( hAPP @ E @ ( c_fst @ B @ C @ D ) ) )
      | ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ C @ F @ D ) @ B )
        = ( hAPP @ ( c_Product__Type_Oapfst @ E @ C @ F @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apfst__eq__conv_1) ).

thf(2636,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_fst @ B @ C @ D ) )
       != ( hAPP @ E @ ( c_fst @ B @ C @ D ) ) )
      | ( ( hAPP @ ( c_Product__Type_Oapfst @ A @ C @ F @ D ) @ B )
        = ( hAPP @ ( c_Product__Type_Oapfst @ E @ C @ F @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(11,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).

thf(807,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OCastThrow_0) ).

thf(2070,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(771,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OFAccThrow_0) ).

thf(2704,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(220,axiom,
    ! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id_0) ).

thf(1410,plain,
    ! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(99,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).

thf(1056,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(618,axiom,
    c_WellTypeRT_OWTrt @ v_P @ v_ha______ @ v_E____ @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ v_a______ ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_F______ @ v_D______ @ ( c_Expr_Oexp_OVal @ v_v______ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RedFAss_I2_J_0) ).

thf(2366,plain,
    c_WellTypeRT_OWTrt @ v_P @ v_ha______ @ v_E____ @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ v_a______ ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_F______ @ v_D______ @ ( c_Expr_Oexp_OVal @ v_v______ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(556,axiom,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(2223,plain,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(62,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).

thf(955,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(7,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I83_J_0) ).

thf(796,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(342,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).

thf(1742,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ F ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(306,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).

thf(1657,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(605,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of__zip__is__None_0) ).

thf(2334,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(775,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ E @ C ) @ E )
        = ( c_Map_Odom @ A @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__dom_0) ).

thf(2714,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ E @ C ) @ E )
        = ( c_Map_Odom @ A @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(407,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
       != ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
      | ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
       != ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
      | ( c_Fun_Oinj__on @ A @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_6) ).

thf(1891,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
       != ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
      | ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
       != ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
      | ( c_Fun_Oinj__on @ A @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(733,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eqD_0) ).

thf(2619,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( c_snd @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(102,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_fequal @ A @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1065,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_fequal @ A @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(607,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ F @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_0) ).

thf(2340,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_fst @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ F @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(138,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).

thf(1165,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(198,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVar @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I121_J_0) ).

thf(1346,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVar @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(484,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ G ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__lcl__add_0) ).

thf(2063,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ G ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(527,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ F ) )
      | ( E = F )
      | ~ ( hBOOL @ ( c_in @ F @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).

thf(2159,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ F ) )
      | ( E = F )
      | ~ ( hBOOL @ ( c_in @ F @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(210,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_1) ).

thf(1378,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(279,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ B @ F @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).

thf(1582,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D )
      | ~ ( c_Fun_Oinj__on @ B @ F @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(446,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D ) @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) @ C @ ( tc_Option_Ooption @ D ) )
       != ( c_Fun_Ofun__upd @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ G @ C @ D ) @ C @ D ) @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ H ) @ C @ ( tc_Option_Ooption @ D ) ) )
      | ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ C ) @ C ) )
      | ( ( c_Nat_Osize__class_Osize @ G @ ( tc_List_Olist @ D ) )
       != ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) )
       != ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) )
      | ( ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D )
        = ( c_Map_Omap__of @ ( c_List_Ozip @ A @ G @ C @ D ) @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__of__zip__upd_0) ).

thf(1976,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D ) @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) @ C @ ( tc_Option_Ooption @ D ) )
       != ( c_Fun_Ofun__upd @ ( c_Map_Omap__of @ ( c_List_Ozip @ A @ G @ C @ D ) @ C @ D ) @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ H ) @ C @ ( tc_Option_Ooption @ D ) ) )
      | ( hBOOL @ ( c_in @ E @ ( c_List_Oset @ A @ C ) @ C ) )
      | ( ( c_Nat_Osize__class_Osize @ G @ ( tc_List_Olist @ D ) )
       != ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) )
       != ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) )
      | ( ( c_Map_Omap__of @ ( c_List_Ozip @ A @ B @ C @ D ) @ C @ D )
        = ( c_Map_Omap__of @ ( c_List_Ozip @ A @ G @ C @ D ) @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(202,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).

thf(1357,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).

thf(992,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(420,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__Ex__1__3 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__paired__Ex_1) ).

thf(1923,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Product__Type__Xsplit__paired__Ex__1__3 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(421,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__restrict__conv_0) ).

thf(1925,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(411,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ ( hAPP @ ( c_Option_Omap @ D @ E @ B ) @ F ) )
      = ( hAPP @ ( c_Option_Omap @ ( c_Fun_Ocomp @ A @ D @ B @ C @ E ) @ E @ C ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__comp_0) ).

thf(1902,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Omap @ A @ B @ C ) @ ( hAPP @ ( c_Option_Omap @ D @ E @ B ) @ F ) )
      = ( hAPP @ ( c_Option_Omap @ ( c_Fun_Ocomp @ A @ D @ B @ C @ E ) @ E @ C ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(621,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__empty__conv_0) ).

thf(2372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(613,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(2353,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(21,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).

thf(839,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(679,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssReds_0) ).

thf(2502,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(513,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ H ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow2_0) ).

thf(2127,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ C ) @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ H ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(380,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).

thf(1829,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ D ) @ E ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).

thf(1129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(647,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
        = ( c_Fun_Oid @ A ) )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__iff_0) ).

thf(2430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
        = ( c_Fun_Oid @ A ) )
      | ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(172,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(1268,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(285,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).

thf(1597,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(71,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).

thf(982,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(402,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

thf(1880,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(670,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).

thf(2484,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(404,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ G ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__lcl__add_0) ).

thf(1885,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F ) @ G ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(1606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OLAssThrow_0) ).

thf(1962,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I220_J_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(340,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_3) ).

thf(1737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(372,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Fun_Ooverride__on @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ G @ F @ ( tc_Option_Ooption @ D ) ) @ C @ ( hAPP @ B @ C ) @ F @ ( tc_Option_Ooption @ D ) )
      = ( c_Fun_Ooverride__on @ A @ B @ ( c_Set_Oinsert @ C @ G @ F ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__upd__lemma_0) ).

thf(1812,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Fun_Ooverride__on @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ G @ F @ ( tc_Option_Ooption @ D ) ) @ C @ ( hAPP @ B @ C ) @ F @ ( tc_Option_Ooption @ D ) )
      = ( c_Fun_Ooverride__on @ A @ B @ ( c_Set_Oinsert @ C @ G @ F ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__comp @ A @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ t_a ) @ v_x @ B @ C @ t_a )
      = ( c_Option_Ooption_ONone @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__empty_I1_J_0) ).

thf(2106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__comp @ A @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ t_a ) @ v_x @ B @ C @ t_a )
      = ( c_Option_Ooption_ONone @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(663,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ A @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).

thf(2470,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ A @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1069,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(415,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ E @ I @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow2_0) ).

thf(1912,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ E @ I @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Exceptions_Opreallocated @ A )
      | ~ ( c_Objects_Ohext @ B @ A )
      | ~ ( c_Exceptions_Opreallocated @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_preallocated__hext_0) ).

thf(882,plain,
    ! [B: $i,A: $i] :
      ( ( c_Exceptions_Opreallocated @ A )
      | ~ ( c_Objects_Ohext @ B @ A )
      | ~ ( c_Exceptions_Opreallocated @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(599,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

thf(2321,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(430,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(1944,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(206,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I185_J_0) ).

thf(1367,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(315,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).

thf(1681,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_2) ).

thf(2074,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ D @ t_a @ t_b ) ) )
      | ( D
        = ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ ( v_sko__Option__Xoption__Xsplit__1 @ A @ C @ D ) ) )
      | ( D
        = ( c_Option_Ooption_ONone @ t_b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(765,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( c_in @ D @ ( c_Map_Oran @ A @ E @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ranI_0) ).

thf(2690,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( c_in @ D @ ( c_Map_Oran @ A @ E @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(239,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).

thf(1463,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(274,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

thf(1565,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(651,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ ( tc_Option_Ooption @ C ) )
        = ( c_Set_Oimage @ A @ F @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ F @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__map__upd_0) ).

thf(2438,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ ( tc_Option_Ooption @ C ) )
        = ( c_Set_Oimage @ A @ F @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ F @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oapsnd @ A @ B @ C )
      = ( c_Product__Type_Oprod__fun @ ( c_Fun_Oid @ C ) @ C @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apsnd__def__raw_0) ).

thf(1037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_Oapsnd @ A @ B @ C )
      = ( c_Product__Type_Oprod__fun @ ( c_Fun_Oid @ C ) @ C @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(731,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ E @ F @ G @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed2_0) ).

thf(2615,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ E @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(354,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
     != ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).

thf(1769,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
     != ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Oid @ B ) @ B @ C @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).

thf(1014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Oid @ B ) @ B @ C @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(223,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
        = ( c_Finite__Set_Osetprod @ ( c_Fun_Oid @ A ) @ ( c_Set_Oimage @ B @ C @ D @ A ) @ A @ A ) )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__reindex__id_0) ).

thf(1417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
        = ( c_Finite__Set_Osetprod @ ( c_Fun_Oid @ A ) @ ( c_Set_Oimage @ B @ C @ D @ A ) @ A @ A ) )
      | ~ ( c_Fun_Oinj__on @ B @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(2975,plain,
    $false,
    inference(cvc4,[status(thm)],[2163,1322,1501,1411,1823,1767,1559,893,941,2280,1686,2612,1469,1168,2295,2306,2131,2031,2412,846,909,1031,2463,1899,2595,2499,2427,1982,1956,1549,1211,2309,1005,2117,2495,2659,1939,1728,2380,1692,1437,2363,1855,2077,994,2527,2671,2676,873,1205,2099,2282,1591,1971,1793,1533,1788,1671,1608,1655,2686,1735,2184,2448,1275,2168,945,1354,1458,2575,1497,2195,1756,1310,1999,2316,1507,2360,2216,2348,2046,1914,1391,1441,2020,973,1935,1645,1475,2173,1803,1482,1887,829,1095,1746,898,2548,1782,1904,1518,1265,1703,1628,1287,1709,2603,1430,2039,2667,2269,1871,2708,1907,1323,802,2682,1313,1455,2562,1992,1132,2571,2703,2698,1760,1330,2444,1860,2274,917,2420,1147,2552,1572,1398,1115,1568,2024,1494,1963,1232,2403,1087,1514,1319,870,2388,2533,2007,2178,924,1714,1450,2090,1109,2259,2650,2451,1864,1828,2555,2017,1489,2237,1415,1677,2540,2034,1183,1283,2508,2190,1447,1622,2137,2103,1943,1600,2205,1696,1843,2058,2367,2437,1928,1072,2530,2523,1796,988,2286,2639,1104,1242,2154,1521,2473,793,2646,1153,810,1338,1708,2641,1730,2083,2621,2660,1868,2061,1636,2441,2589,1223,2601,2560,2249,2596,1255,1217,1751,1666,2606,2032,2414,2396,1883,2264,2409,1042,952,1123,862,1174,2133,788,1619,1370,1238,2015,1423,2670,1920,1951,1687,1159,2327,2345,2313,1281,1634,2433,2477,2565,879,2663,2332,2068,1819,2200,2609,1836,2181,1195,2211,1407,2112,1291,1740,1910,842,2653,1106,1360,2300,2115,948,1953,1064,1587,1425,2509,1118,1762,2515,1772,1259,1375,1121,1878,2631,1138,2537,2460,884,1028,1361,2323,2312,2240,1584,1937,1214,2108,2666,1889,1744,901,1075,1016,2085,2649,1039,970,2304,1831,2505,2497,1947,1984,1874,2052,1720,2272,2140,1759,2370,1825,2285,2504,1099,985,1150,1478,1297,2681,1530,1539,1382,1668,1974,1552,2243,2355,1192,1932,1060,1050,2581,2465,1002,1852,1979,779,1333,1202,1695,921,1466,2221,2617,2662,2423,926,1434,1857,1814,938,2208,805,1846,1054,2408,1663,1278,1135,2001,1764,2176,2292,2391,2717,2028,2524,1631,2121,2235,906,1959,2556,2253,2149,819,1916,2048,2225,2525,2489,1388,826,958,1701,1615,1784,1652,1929,2674,2568,2695,1226,1865,1733,1997,1092,2706,2425,2474,2193,1786,2166,1090,2457,1897,2573,2148,979,2521,784,1011,1524,1048,996,1801,2065,1209,2119,2151,2229,2214,2383,2624,1894,2493,1349,2097,2246,1603,1722,1144,2378,1690,2197,1969,1307,1080,858,2129,816,1821,2446,1862,848,1838,895,964,915,1344,1022,2278,1177,890,2180,799,1162,1556,2542,1460,2329,932,1112,2578,2418,2350,2171,1066,2288,2592,1364,2156,2693,1562,912,1171,1198,1841,1699,2401,1594,2051,2550,1245,2481,2633,2022,2535,2101,851,1102,1973,1805,2054,1034,1809,2614,1203,944,2318,1420,2037,1684,2124,1509,2629,1472,823,836,1304,1873,1990,2684,2202,1018,2256,2513,1748,855,1025,887,1780,1098,1798,2298,1611,2375,1156,2060,1400,2143,2012,1941,1252,2678,2518,1753,2386,2569,2092,2165,2337,2044,1579,1336,2656,1711,1790,1987,1716,2454,1300,1452,2688,2700,1186,1262,1235,2276,2219,2486,951,2545,2599,2468,1220,2500,1543,1849,864,1427,1504,2511,1717,1372,1272,2584,2056,1404,2247,2558,2113,1141,1536,1353,2357,1955,2145,1485,1052,2711,2722,1008,2266,876,991,1617,2435,2479,2088,1180,1966,1949,1817,1517,2325,1126,2071,1807,2626,1918,1316,1649,2352,1084,2078,1834,976,903,2490,2187,1189,2110,2342,1575,2226,2643,1590,1326,2389,1341,2554,2004,2026,781,2416,2262,2394,961,813,1385,1674,1639,2290,2251,2135,2406,2009,1491,2081,2475,1777,1294,929,2198,2576,1706,2183,1661,2095,2230,1444,1994,1045,2421,2399,2041,1077,2162,999,1642,2302,1725,1957,1678,2587,1546,1876,1527,867,1480,1512,1774,833,967,2719,1229,2233,1395,1625,1248,790,2636,807,2070,2704,1410,1056,2366,2223,955,796,1742,1657,2334,2714,1891,2619,1065,2340,1165,1346,2063,2159,1378,1582,1976,1357,992,1923,1925,1902,2372,2353,839,2502,2127,1829,1129,2430,1268,1597,982,1880,2484,1885,1606,1962,935,1737,1812,2106,2470,1069,1912,882,2321,1944,1367,1681,2074,2690,1463,1565,2438,1037,2615,1769,1014,1417]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV921-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri May 19 02:43:51 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.87/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.90/1.10  % [INFO] 	 Parsing done (268ms). 
% 1.90/1.11  % [INFO] 	 Running in sequential loop mode. 
% 2.47/1.31  % [INFO] 	 eprover registered as external prover. 
% 2.47/1.31  % [INFO] 	 cvc4 registered as external prover. 
% 2.47/1.32  % [INFO] 	 Scanning for conjecture ... 
% 3.18/1.52  % [INFO] 	 Found a conjecture and 777 axioms. Running axiom selection ... 
% 4.21/1.78  % [INFO] 	 Axiom selection finished. Selected 777 axioms (removed 0 axioms). 
% 5.45/2.15  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.45/2.17  % [INFO] 	 Type checking passed. 
% 5.45/2.17  % [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 ... 
% 19.46/5.63  % External prover 'cvc4' found a proof!
% 19.46/5.63  % [INFO] 	 Killing All external provers ... 
% 19.46/5.63  % Time passed: 5120ms (effective reasoning time: 4523ms)
% 19.46/5.63  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 19.46/5.64  % Axioms used in derivation (777): cls_red__reds_ORedInitBlock_0, cls_red__lcl__add_0, cls_exp_Osimps_I56_J_0, cls_exp_Osimps_I118_J_0, cls_inj__Some_0, cls_red__reds_OInitBlockThrow_0, cls_set__empty__eq_1, cls_bot__fun__eq_0, cls_exp_Osimps_I184_J_0, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_option_Oinject_0, cls_map__le__upd_0, cls_Diff__cancel_0, cls_option_Osplit_3, cls_map__upd__eqD1_0, cls_split__beta_0, cls_exp_Osimps_I156_J_0, cls_val_Osimps_I3_J_0, cls_exp_Osimps_I9_J_1, cls_CallObjThrow_0, cls_Diff__iff_2, cls_restrict__map__to__empty_0, cls_red__reds_OLAssThrow_0, cls_rtrancl__idemp_0, cls_exp_Osimps_I92_J_0, cls_FAcc_0, cls_snd__conv_0, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I103_J_0, cls_image__constant_0, cls_red__reds_OFAssRed2_0, cls_inj__iff_1, cls_insertE_0, cls_splitD_H_0, cls_internal__split__def_0, cls_CallRedsThrowObj_0, cls_redp__redsp_OThrowRed_0, cls_redp__redsp_OCastThrow_0, cls_apsnd__conv_0, cls_exp_Osimps_I213_J_0, cls_val_Osimps_I10_J_0, cls_split__comp_0, cls_map__add__None_2, cls_exp_Osimps_I218_J_0, cls_snd__eqD_0, cls_id__o_0, cls_inj__on__image__iff_4, cls_exp_Osimps_I72_J_0, cls_ospec_1, cls_the__inv__f__f_0, cls_inj__image__eq__iff_0, cls_eval__evals_OFAssThrow2_0, cls_inv__into__comp_0, cls_map__upd__Some__unfold_4, cls_fun__upd__image_1, cls_red__reds_OFAssRed1_0, cls_eval__cases_I1_J_1, cls_redp__redsp_OFAssRed1_0, cls_exp_Osimps_I193_J_0, cls_CastReds_0, cls_map__add__assoc_0, cls_set__ConsD_0, cls_exp_Osimps_I10_J_1, cls_exp_Osimps_I225_J_0, cls_exp_Osimps_I138_J_0, cls_exp_Osimps_I81_J_0, cls_swap__def_0, cls_exp_Osimps_I137_J_0, cls_BinOpRedsThrow2_0, cls_exp_Osimps_I128_J_0, cls_empty__is__image_1, cls_exp_Osimps_I165_J_0, cls_exp_Osimps_I7_J_2, cls_insert__code_1, cls_map__le__trans_0, cls_LAss_0, cls_fun__upd__apply_1, cls_redp__redsp_OThrowThrow_0, cls_redp__redsp_OSeqRed_0, cls_exp_Osimps_I204_J_0, cls_CallRedsObj_0, cls_exp_Osimps_I219_J_0, cls_exp_Osimps_I149_J_0, cls_lconf__hext_0, cls_prod_Ocases_0, cls_exp_Osimps_I190_J_0, cls_Option_Oset_Osimps_I2_J_0, cls_exp_Osimps_I11_J_0, cls_lconf__def_0, cls_exp_Osimps_I15_J_1, cls_list_Oinject_0, cls_oconf__new_0, cls_BinOpRedsThrow1_0, cls_map__upd__Some__unfold_3, cls_map__upds__apply__nontin_0, cls_map__of__Cons__code_I2_J_1, cls_CHAINED_0, cls_restrict__fun__upd_0, cls_eval__evals_OCondThrow_0, cls_COMBK__def_0, cls_exp_Osimps_I221_J_0, cls_map__comp__simps_I2_J_0, cls_insert__absorb_0, cls_apfst__def_0, cls_hconf__new_0, cls_exp_Osimps_I115_J_0, cls_redp__redsp_OCallObj_0, cls_hext__def_0, cls_exp_Osimps_I211_J_0, cls_hconf__def_3, cls_option_Osimps_I2_J_0, cls_BinOp2Reds_0, cls_empty__iff_0, cls_not__Cons__self2_0, cls_surjective__pairing_0, clsarity_bool__HOL_Ominus, cls_hconfD_0, cls_o__eq__id__dest_0, cls_the__inv__into__onto_0, cls_restrict__map__insert_0, cls_rtrancl__trans_0, cls_map__le__iff__map__add__commute_0, cls_mem__def_1, cls_fun__upd__image_0, cls_map__comp__empty_I2_J_0, cls_FAssReds2_0, cls_split__curry_0, cls_exp_Osimps_I13_J_0, cls_exp_Osimps_I154_J_0, cls_LAssReds_0, cls_COMBI__def__raw_0, cls_filter__eq__ConsD_2, cls_exp_Osimps_I185_J_0, cls_fun__upd__None__restrict_0, cls_exp_Osimps_I141_J_0, cls_exp_Osimps_I49_J_0, cls_dom__fun__upd_0, cls_splitI_0, cls_exp_Osimps_I97_J_0, cls_exp_Osimps_I170_J_0, cls_exp_Osimps_I199_J_0, cls_insert__iff_1, cls_swap__commute_0, cls_SeqReds2_0, cls_exp_Osimps_I208_J_0, cls_red__reds_OFAssThrow2_0, cls_exp_Osimps_I188_J_0, cls_K__record__comp_0, cls_RedFAss_Ohyps_0, cls_map__of__Cons__code_I2_J_0, cls_map__comp__None__iff_0, cls_apsnd__apfst__commute_0, cls_Diff__insert_0, cls_insert__Diff__if_1, cls_exp_Osimps_I109_J_0, cls_unfold__while_0, cls_exp_Osimps_I212_J_0, cls_typeof__conf_0, cls_map__add__Some__iff_3, cls_inj__image__mem__iff_0, cls_exp_Osimps_I8_J_3, cls_filter_Osimps_I2_J_0, cls_redp__redsp_OCondThrow_0, cls_redp__redsp_ORedInitBlock_0, cls_map__le__empty_0, cls_exp_Osimps_I178_J_0, cls_inj__on__image__iff_5, cls_redp__redsp_OCallThrowObj_0, cls_red__reds_OInitBlockRed_0, cls_is__none__def__raw_0, cls_map__of__zip__is__None_1, clsarity_fun__Orderings_Otop, cls_exp_Osimps_I2_J_1, cls_f__inv__into__f_0, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I206_J_0, cls_redp__redsp_ORedFAcc_0, cls_exp_Osimps_I194_J_0, cls_exp_Osimps_I223_J_0, cls_exp_Osimps_I124_J_0, cls_snd__apfst_0, cls_exp_Osimps_I4_J_1, cls_RedFAss_I3_J_0, cls_prod__case__split_0, cls_red__reds_OCallThrowObj_0, cls_red__reds_OLAssRed_0, cls_exp_Osimps_I157_J_0, cls_exp_Osimps_I113_J_0, cls_exI__realizer_0, cls_exp_Osimps_I11_J_1, cls_scomp__apply_0, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_exp_Osimps_I171_J_0, cls_redp__redsp_ORedFAss_0, cls_empty__is__image_0, cls_eval__evals_OSeqThrow_0, cls_converse__rtrancl__into__rtrancl_0, cls_CondReds_0, cls_inj__on__insert_0, cls_Diff__UNIV_0, cls_map__upd__Some__unfold_0, cls_rangeI_0, cls_exp_Osimps_I67_J_0, cls_exp_Osimps_I131_J_0, cls_conf__upd__obj_1, cls_exp_Osimps_I4_J_0, cls_rev__image__eqI_0, cls_exp_Osimps_I5_J_0, cls_is__none__code_I2_J_0, cls_override__on__upd__lemma_0, clsarity_fun__Orderings_Obot, cls_redp__redsp_OInitBlockThrow_0, cls_hext__trans_0, cls_f__the__inv__into__f_0, cls_exp_Osimps_I160_J_0, cls_hext__upd__obj_0, cls_fun__upd__other_0, cls_exp_Osimps_I84_J_0, cls_exp_Osimps_I209_J_0, cls_map__le__def_0, cls_apsnd__compose_0, cls_image__id_0, cls_redp__redsp_OFAssRed2_0, cls_exp_Osimps_I142_J_0, cls_fst__eqD_0, cls_red__reds_OThrowThrow_0, cls_red__reds_OCallObj_0, cls_exp_Osimps_I116_J_0, cls_insert__ident_0, cls_WhileRedsThrow_0, cls_redp__redsp_OFAccThrow_0, cls_image__constant__conv_1, cls_hext__refl_0, cls_redp__redsp_OFAssThrow1_0, cls_inv__f__eq_0, cls_map__comp__simps_I1_J_0, cls_dom__const_0, cls_option_Ocase__cong_3, cls_redp__redsp_OBinOpThrow1_0, cls_exp_Osimps_I74_J_0, cls_id__apply_0, cls_map__add__upd__left_0, cls_exp_Osimps_I110_J_0, cls_apfst__conv_0, cls_exp_Osimps_I123_J_0, cls_exp_Osimps_I134_J_0, cls_inv__image__comp_0, cls_exp_Osimps_I205_J_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_eval__evals_OBinOpThrow2_0, cls_eval__evals_OFAccThrow_0, cls_override__on__apply__notin_0, cls_exp_Osimps_I176_J_0, cls_exp_Osimps_I143_J_0, cls_not__None__eq_1, cls_swap__nilpotent_0, cls_exp_Osimps_I146_J_0, cls_exp_Osimps_I174_J_0, cls_fst__apsnd_0, cls_map__add__dom__app__simps_I2_J_0, cls_WhileCondThrow_0, cls_exp_Osimps_I139_J_0, cls_exp_Osimps_I10_J_2, cls_comp__inj__on_0, cls_redp__redsp_OTryRed_0, cls_exp_Osimps_I148_J_0, cls_hconf__upd__obj_0, cls_red__reds_OBinOpThrow1_0, cls_inj__iff_0, cls_exp_Osimps_I172_J_0, cls_swap__self_0, cls_option_Osplit__asm_3, cls_ThrowReds_0, cls_inj__on__imageI_0, cls_oconf__fupd_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_curryI_0, cls_curry__split_0, cls_map__upds__Cons_0, cls_WTrt__hext__mono_0, cls_elem__set_1, cls_prod_Orecs_0, cls_insert__Diff__single_0, cls_image__map__upd_0, cls_singleton__iff_1, cls_insert__code_2, cls_exp_Osimps_I46_J_0, cls_CHAINED_0_01, cls_FAccRedsVal_0, cls_map__le__refl_0, cls_Diff__idemp_0, cls_exp_Osimps_I99_J_0, cls_List_Oset_Osimps_I2_J_0, cls_eval__evals_OFAssThrow1_0, cls_redp__redsp_ORedTry_0, cls_redp__redsp_OBlockThrow_0, cls_red__reds_OTryRed_0, cls_inv__into__f__f_0, cls_preallocated__upd__obj_0, cls_map__le__upds_0, cls_UNIV__not__empty_0, cls_exp_Osimps_I180_J_0, cls_the_Osimps_0, cls_red__reds_ORedBlock_0, cls_exp_Osimps_I77_J_0, cls_map__add__dom__app__simps_I3_J_0, cls_redp__redsp_ORedLAss_0, cls_image__insert_0, cls_exp_Osimps_I69_J_0, cls_map__of__zip__is__None_0, cls_exp_Osimps_I98_J_0, cls_exp_Osimps_I61_J_0, cls_exp_Osimps_I15_J_0, cls_exp_Osimps_I183_J_0, cls_doubleton__eq__iff_2, cls_map__upd__nonempty_0, cls_exp_Osimps_I132_J_0, cls_FAccReds_0, cls_fun__upd__triv_0, cls_option_Orecs_I2_J_0, cls_exp_Osimps_I12_J_2, cls_apsnd__eq__conv_1, cls_red__reds_ORedVar_0, cls_inj__on__image__iff_2, cls_Seq_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_ran__empty_0, cls_exp_Osimps_I207_J_0, cls_map__upds__twist_0, clsarity_nat__Orderings_Obot, cls_exp_Osimps_I83_J_0, cls_exp_Osimps_I2_J_0, cls_setprod__reindex__id_0, cls_ex__in__conv_0, cls_exp_Osimps_I76_J_0, cls_exp_Osimps_I70_J_0, cls_option__map__None_0, cls_red__reds_ORedWhile_0, cls_exp_Osimps_I8_J_2, cls_ranI_0, cls_exp_Osimps_I177_J_0, cls_FAssRedsThrow2_0, cls_dom__eq__empty__conv_0, cls_fst__apfst_0, cls_swap__triple_0, cls_inj__on__the__inv__into_0, cls_apfst__eq__conv_1, cls_is__none__def_0, cls_exp_Osimps_I89_J_0, cls_exp_Osimps_I159_J_0, cls_map__comp__Some__iff_2, cls_fun__upd__restrict__conv_0, cls_conf__upd__obj_0, cls_option_Osplit_2, cls_red__reds_OBinOpRed2_0, cls_TryReds_0, cls_exp_Osimps_I186_J_0, cls_exp_Osimps_I210_J_0, cls_exp_Osimps_I105_J_0, cls_exp_Osimps_I220_J_0, cls_map__add__None_0, cls_exp_Osimps_I62_J_0, cls_inj__on__image__iff_6, cls_Pair__scomp_0, cls_exp_Osimps_I112_J_0, cls_exp_Osimps_I122_J_0, cls_CondRedsThrow_0, cls_Pair__fst__snd__eq_0, cls_not__Cons__self_0, cls_exp_Osimps_I135_J_0, cls_map__add__le__mapE_0, cls_comp__swap_0, cls_lconf__def_3, cls_RedFAss_I2_J_0, cls_exp_Osimps_I158_J_0, cls_redp__redsp_OSeqThrow_0, cls_unfold__while_1, cls_red__reds_ORedLAss_0, cls_image__empty_0, cls_dom__eq__singleton__conv_0, cls_exp_Osimps_I60_J_0, cls_option_Osplit__asm_2, cls_map__of__filter__in_0, cls_exp_Osimps_I162_J_0, cls_inj__on__insert_1, cls_exp_Osimps_I201_J_0, cls_exp_Osimps_I166_J_0, cls_map__upd__Some__unfold_1, cls_red__reds_OFAssThrow1_0, cls_TryRedsVal_0, cls_option_Osimps_I4_J_0, cls_exp_Osimps_I47_J_0, cls_map__add__upds_0, cls_exp_Osimps_I7_J_1, cls_exp_Osimps_I189_J_0, cls_image__constant__conv_0, cls_exp_Osimps_I224_J_0, cls_inj__on__swap__iff_0, cls_exp_Osimps_I15_J_3, cls_insertI1_0, cls_eval__evals_OThrowThrow_0, cls_DiffI_0, cls_red__reds_OBinOpRed1_0, cls_exp_Osimps_I169_J_0, cls_map__upd__triv_0, cls_split__case__cert_0, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_internal__split__conv_0, cls_rtrancl__eq__or__trancl_1, cls_exp_Osimps_I55_J_0, cls_FAss_0, cls_empty__not__insert_0, cls_red__reds_OBlockThrow_0, cls_insert__Diff1_0, cls_WTrtSeq_0, cls_empty__map__add_0, cls_redp__redsp_OLAssThrow_0, cls_dom__empty_0, cls_exp_Osimps_I101_J_0, cls_exp_Osimps_I102_J_0, cls_CastRedsThrow_0, cls_exp_Osimps_I75_J_0, cls_inv__id_0, cls_the__inv__into__comp_0, cls_red__reds_OSeqRed_0, cls_image__ident_0, cls_exp_Osimps_I80_J_0, cls_exp_Osimps_I145_J_0, cls_exp_Osimps_I59_J_0, cls_fun__upd__twist_0, cls_SeqRedsThrow_0, cls_doubleton__eq__iff_0, cls_override__on__apply__in_0, cls_Diff__insert2_0, cls_option_Osplit_5, cls_option_Ocase__cong_0, cls_prod__caseI_0, cls_apsnd__def__raw_0, cls_Pair__eq_0, cls_exp_Osimps_I129_J_0, cls_singletonE_0, cls_insert__Diff_0, cls_inj__on__empty_0, cls_elem__set_0, cls_image__iff_2, cls_fun__upd__apply_0, cls_LAssRedsThrow_0, cls_image__set__diff_0, cls_redp__redsp_OCondRed_0, cls_exp_Osimps_I68_J_0, cls_inj__on__iff_0, cls_ran__map__upd_0, cls_not__Some__eq_1, cls_red__reds_ORedFAcc_0, cls_insert__dom_0, cls_UNIV__I_0, cls_DiffE_0, cls_insertCI_0, cls_exp_Osimps_I182_J_0, cls_dom__eq__singleton__conv_1, cls_exp_Osimps_I133_J_0, cls_map__le__antisym_0, cls_curryD_0, cls_restrict__in_0, cls_exp_Osimps_I114_J_0, cls_apsnd__apfst_0, cls_exp_Osimps_I121_J_0, cls_bot1E_0, cls_option_Osplit_1, cls_exp_Osimps_I216_J_0, cls_apfst__apsnd_0, cls_exp_Osimps_I203_J_0, cls_domI_0, cls_exp_Osimps_I57_J_0, cls_o__eq__dest_0, cls_red__reds_OCastThrow_0, cls_bex__empty_0, cls_scomp__Pair_0, cls_exp_Osimps_I4_J_2, cls_top1I_0, cls_redp__redsp_OBinOpRed1_0, cls_exp_Osimps_I191_J_0, cls_lconf__def_1, cls_eval__evals_OCastThrow_0, cls_o__eq__dest__lhs_0, cls_redp__redsp_OBinOpRed2_0, cls_inj__on__fun__updI_0, cls_exp_Osimps_I53_J_0, cls_exp_Osimps_I152_J_0, cls_exp_Osimps_I50_J_0, cls_exp_Osimps_I215_J_0, cls_id__def_0, cls_doubleton__eq__iff_3, cls_map__comp__None__iff_3, cls_oconf__upd__obj_0, cls_exp_Osimps_I93_J_0, cls_domIff_0, cls_SeqReds_0, cls_lconf__def_2, cls_option_Ocase__cong_1, cls_exp_Osimps_I73_J_0, cls_Var_0, cls_inj__on__def_0, cls_exp_Osimps_I126_J_0, cls_inj__on__imp__inj__on__swap_0, cls_eval__evals_OLAssThrow_0, cls_red__reds_OThrowRed_0, cls_map__add__SomeD_0, cls_exp_Osimps_I95_J_0, cls_split__paired__All_0, cls_fun__upd__restrict_0, cls_exp_Osimps_I54_J_0, cls_map__add__upd_0, cls_apsnd__eq__conv_0, cls_exp_Osimps_I8_J_1, cls_exp_Osimps_I117_J_0, cls_hext__objD_0, cls_map__le__imp__upd__le_0, cls_exp_Osimps_I179_J_0, cls_red__reds_OFAccRed_0, cls_override__on__emptyset_0, cls_injD_0, cls_conf__hext_0, cls_CHAINED_0_02, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, cls_val_Osimps_I11_J_0, cls_exp_Osimps_I86_J_0, cls_inj__on__map__add__dom_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_exp_Osimps_I58_J_0, cls_apfst__eq__conv_0, cls_exp_Osimps_I106_J_0, cls_map__add__empty_0, cls_option__map__is__None_0, cls_exp_Osimps_I6_J_0, cls_exp_Osimps_I108_J_0, cls_insert__not__empty_0, cls_red__reds_OBinOpThrow2_0, cls_prod__eqI_0, cls_exp_Osimps_I90_J_0, cls_o__def_0, cls_inj__on__image__iff_7, cls_exp_Osimps_I127_J_0, cls_exp_Osimps_I66_J_0, cls_o__id_0, cls_exp_Osimps_I222_J_0, cls_prod_Osplit_0, cls_FAssRedsVal_0, cls_fun__diff__def_0, cls_inj__on__swap__iff_1, cls_scomp__def_0, cls_exp_Osimps_I155_J_0, cls_eval__cases_I1_J_0, cls_doubleton__eq__iff_1, cls_eval__evals_OBinOpThrow1_0, cls_fun__upd__idem__iff_0, cls_restrict__out_0, cls_split__paired__Ex_1, cls_insert__absorb2_0, cls_Product__Type_Osplit_0, cls_inj__on__image__iff_1, cls_FAccRedsThrow_0, cls_hconf__def_1, cls_fun__upd__idem_0, cls_redp__redsp_OFAccRed_0, cls_FAssRedsThrow1_0, cls_red__preserves__hconf_0, cls_inj__on__id_0, cls_red__reds_OCondThrow_0, cls_prod__fun_0, cls_rtrancl_Ortrancl__refl_0, cls_exp_Osimps_I71_J_0, cls_exp_Osimps_I12_J_1, cls_map__comp__empty_I1_J_0, cls_the__inv__into__f__eq_0, cls_option_Osplit__asm_1, cls_pair__collapse_0, cls_exp_Osimps_I82_J_0, cls_splitD_0, cls_exp_Osimps_I14_J_0, cls_WTrtVal_0, cls_exp_Osimps_I167_J_0, cls_redp__redsp_OFAssThrow2_0, cls_set__empty__eq_0, cls_inv__into__injective_0, cls_redp__redsp_OInitBlockRed_0, cls_filter__id__conv_0, cls_exp_Osimps_I125_J_0, cls_ospec_0, cls_dom__minus_0, cls_exp_Osimps_I107_J_0, cls_Diff__empty_0, cls_exp_Osimps_I120_J_0, cls_exp_Osimps_I9_J_2, cls_prod_Osplit__asm_0, cls_exp_Osimps_I161_J_0, cls_comp__cong_0, cls_exp_Osimps_I151_J_0, cls_exp_Osimps_I217_J_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_snd__apsnd_0, cls_list_Oinject_1, cls_exp_Osimps_I45_J_0, cls_setsum__reindex__id_0, cls_map__upd__Some__unfold_2, cls_exp_Osimps_I8_J_0, cls_exp_Osimps_I44_J_0, cls_ThrowRedsThrow_0, cls_exp_Osimps_I192_J_0, cls_option_Osplit_4, cls_exp_Osimps_I7_J_0, cls_emptyE_0, cls_preallocated__new_0, cls_fun__upd__same_0, cls_is__none__def_1, cls_o__inv__o__cancel_0, cls_eq__eqI_1, cls_redp__redsp_ORedBlock_0, cls_map__comp__None__iff_1, cls_comm__monoid__add_Ononempty__iff_2, cls_map__add__dom__app__simps_I1_J_0, cls_exp_Osimps_I153_J_0, cls_singleton__inject_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_exp_Osimps_I164_J_0, cls_exp_Osimps_I6_J_1, cls_red__reds_OSeqThrow_0, cls_exp_Osimps_I65_J_0, cls_inj__on__image__iff_3, cls_option_Osimps_I3_J_0, cls_option__map__o__empty_0, cls_BinOp1Reds_0, cls_inj__onD_0, cls_restrict__fun__upd_1, cls_Try_0, cls_fun__upd__None__restrict_1, cls_exp_Osimps_I51_J_0, cls_empty__upd__none_0, cls_red__hext__incr_0, cls_inj__on__contraD_0, cls_exp_Osimps_I111_J_0, cls_exp_Osimps_I52_J_0, cls_exp_Osimps_I130_J_0, cls_red__reds_OCastRed_0, cls_Val_0, cls_exp_Osimps_I15_J_2, cls_r__into__rtrancl_0, cls_mem__splitI_0, cls_option_Osplit__asm_5, cls_eval__hext_0, cls_exp_Osimps_I64_J_0, cls_exp_Osimps_I88_J_0, cls_exp_Osimps_I187_J_0, cls_setprod__reindex_0, cls_image__eqI_0, cls_FAssReds1_0, cls_the__inv__into__f__f_0, cls_conjI__realizer_1, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_inv__into__into_0, cls_insertCI_1, cls_red__reds_OFAccThrow_0, cls_option_Orecs_I1_J_0, cls_exp_Osimps_I10_J_0, cls_option_Osplit_0, cls_curry__conv_0, cls_doubleton__eq__iff_4, cls_exp_Osimps_I96_J_0, cls_map__of__zip__is__Some_1, cls_insert__code_0, cls_map__add__find__right_0, cls_map__of_Osimps_I2_J_0, cls_exp_Osimps_I196_J_0, cls_inj__on__id2_0, cls_exp_Osimps_I91_J_0, cls_option__map__o__map__upd_0, cls_option_Osplit__asm_4, cls_exp_Osimps_I200_J_0, cls_exp_Osimps_I119_J_0, cls_domIff_1, cls_map__add__Some__iff_2, cls_DiffE_1, cls_dom__fun__upd_1, cls_apfst__compose_0, cls_exp_Osimps_I214_J_0, cls_exp_Osimps_I168_J_0, cls_inj__on__image__iff_0, cls_inv__f__f_0, cls_Throw_0, cls_exp_Osimps_I181_J_0, cls_redp__redsp_ORedWhile_0, cls_exp_Osimps_I63_J_0, cls_option_Ocase__cong_2, cls_fun__upd__upd_0, cls_map__le__map__add_0, cls_red__reds_ORedFAss_0, cls_map__of__zip__upd_0, cls_redp__redsp_ORedVar_0, cls_zip__Cons__Cons_0, cls_map__add__SomeD_1, cls_redp__redsp_OLAssRed_0, cls_insert__commute_0, cls_insert__iff_2, cls_Diff__insert__absorb_0, cls_preallocated__hext_0, cls_conjI__realizer_0, cls_setsum__reindex_0, cls_insert__image_0, cls_red__reds_OCondRed_0, cls_map__le__iff__map__add__commute_1, cls_apsnd__def_0, cls_exp_Osimps_I140_J_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_COMBI__def_0, cls_Red__lcl__add_0, cls_exp_Osimps_I87_J_0, cls_exp_Osimps_I78_J_0, cls_restrict__map__empty_0, cls_option__map__Some_0, cls_image__is__empty_0, cls_exp_Osimps_I202_J_0, cls_filter_Osimps_I2_J_1, cls_Pair__eq_1, cls_exp_Osimps_I173_J_0, cls_imageI_0, cls_prod__case__beta_0, cls_exp_Osimps_I48_J_0, cls_exp_Osimps_I104_J_0, cls_map__comp__None__iff_2, cls_hext__typeof__mono_0, cls_exp_Osimps_I198_J_0, cls_image__compose_0, cls_exp_Osimps_I94_J_0, cls_inj__on__map__add__dom_1, cls_hext__new_0, cls_exp_Osimps_I12_J_0, cls_exp_Osimps_I100_J_0, cls_option_Osimps_I5_J_0, cls_redp__redsp_OCastRed_0, cls_exp_Osimps_I163_J_0, cls_red__reds_ORedSeq_0, clsarity_fun__HOL_Ominus, cls_Cons__eq__filterD_2, cls_upd__None__map__le_0, cls_o__apply_0, cls_option__map__comp_0, cls_setprod__reindex__cong_0, cls_map__add__le__mapI_0, clsarity_bool__Orderings_Otop, cls_ball__empty_0, cls_fun__upd__comp_0, cls_exp_Osimps_I147_J_0, cls_exp_Osimps_I3_J_0, cls_map__add__None_1, cls_red__reds_ORedTry_0, cls_exp_Osimps_I197_J_0, cls_o__assoc_0, cls_redp__redsp_ORedSeq_0, cls_WTrtVar_0, cls_inv__into__f__eq_0, cls_redp__redsp_OBinOpThrow2_0, cls_empty__Diff_0, cls_exp_Osimps_I13_J_1, cls_fun__upd__idem__iff_1, cls_LAssRedsVal_0, clsarity_nat__HOL_Ominus, cls_oconf__hext_0, cls_image__inv__f__f_0, cls_fst__conv_0, cls_lconf__upd_0
% 19.46/5.64  % No. of inferences in proof: 1557
% 19.46/5.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5120 ms resp. 4523 ms w/o parsing
% 20.66/6.17  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.66/6.18  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------