TSTP Solution File: SWV919-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV919-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 12:19:24 EDT 2023
% Result : Unsatisfiable 83.11s 20.55s
% Output : Refutation 83.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 576
% Syntax : Number of formulae : 1033 ( 359 unt; 120 typ; 0 def)
% Number of atoms : 1753 ( 902 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 17346 ( 766 ~; 840 |; 0 &;15740 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 311 ( 311 >; 0 *; 0 +; 0 <<)
% Number of symbols : 122 ( 120 usr; 24 con; 0-6 aty)
% Number of variables : 4126 ( 0 ^;4126 !; 0 ?;4126 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Conform_Ooconf_type,type,
c_Conform_Ooconf: $i > $i > $i > $i > $o ).
thf(v_P_type,type,
v_P: $i ).
thf(v_ha_____type,type,
v_ha____: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $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_prod_type,type,
tc_prod: $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(v_C_____type,type,
v_C____: $i ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $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(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
thf(v_v_____type,type,
v_v____: $i ).
thf(tc_Expr_Oexp_type,type,
tc_Expr_Oexp: $i > $i ).
thf(c_TypeRel_Owiden_type,type,
c_TypeRel_Owiden: $i > $i > $i > $i > $o ).
thf(c_Conform_Osko__Conform__Xconf__def__1__1_type,type,
c_Conform_Osko__Conform__Xconf__def__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Conform_Oconf_type,type,
c_Conform_Oconf: $i > $i > $i > $i > $i > $o ).
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_OFAss_type,type,
c_Expr_Oexp_OFAss: $i > $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_OFAcc_type,type,
c_Expr_Oexp_OFAcc: $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_Set_Oinsert_type,type,
c_Set_Oinsert: $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_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
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_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(tc_bool_type,type,
tc_bool: $i ).
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_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_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_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_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $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(tc_nat_type,type,
tc_nat: $i ).
thf(c_Expr_Oexp_OVal_type,type,
c_Expr_Oexp_OVal: $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_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: $i > $i > $i > $i > $i > $o ).
thf(c_Progress_OWTrt_H_type,type,
c_Progress_OWTrt_H: $i > $i > $i > $i > $i > $o ).
thf(c_TypeRel_OFields_type,type,
c_TypeRel_OFields: $i > $i > $i > $i > $o ).
thf(c_TypeRel_Osko__TypeRel__Xhas__field__def__1__1_type,type,
c_TypeRel_Osko__TypeRel__Xhas__field__def__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(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_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_Objects_Otypeof__h_type,type,
c_Objects_Otypeof__h: $i > $i > $i ).
thf(tc_Type_Oty_type,type,
tc_Type_Oty: $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
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(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(c_COMBK_type,type,
c_COMBK: $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(c_Map_Omap__of_type,type,
c_Map_Omap__of: $i > $i > $i > $i ).
thf(c_Hilbert__Choice_Oinv__into_type,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
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(v_Tv_____type,type,
v_Tv____: $i ).
thf(v_TF_____type,type,
v_TF____: $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(c_SmallStep_Oredp_type,type,
c_SmallStep_Oredp: $i > $i > $i > $i > $i > $o ).
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_BigStep_Oeval_type,type,
c_BigStep_Oeval: $i > $i > $i > $i > $i > $o ).
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_Objects_Osko__Objects__Xhext__objD__1__1_type,type,
c_Objects_Osko__Objects__Xhext__objD__1__1: $i > $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_E_____type,type,
v_E____: $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_T_____type,type,
v_T____: $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_Objects_Oinit__fields_type,type,
c_Objects_Oinit__fields: $i > $i ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1501,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)],[432]) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_map__of__Cons__code_I2_J_0) ).
thf(1411,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)],[396]) ).
thf(414,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_2) ).
thf(1454,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)],[414]) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(909,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)],[190]) ).
thf(183,axiom,
c_TypeRel_Owiden @ v_P @ v_Tv____ @ v_TF____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sub_0) ).
thf(893,plain,
c_TypeRel_Owiden @ v_P @ v_Tv____ @ v_TF____ @ ( 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)],[183]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I4_J_0) ).
thf(518,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)],[28]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).
thf(555,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)],[45]) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_5) ).
thf(1168,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)],[297]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_prod_Orecs_0) ).
thf(760,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)],[130]) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__None__iff_2) ).
thf(1237,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)],[324]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_4) ).
thf(846,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)],[164]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_setsum__reindex_0) ).
thf(666,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)],[91]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_option_Ocase__cong_2) ).
thf(1295,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)],[348]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1554,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)],[455]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).
thf(1110,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)],[273]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
thf(977,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)],[217]) ).
thf(229,axiom,
c_TypeRel_Ohas__field @ v_P @ v_C____ @ v_F____ @ v_TF____ @ v_D____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has_0) ).
thf(1005,plain,
c_TypeRel_Ohas__field @ v_P @ v_C____ @ v_F____ @ v_TF____ @ v_D____ @ ( 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)],[229]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(730,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)],[118]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict_0) ).
thf(1068,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)],[256]) ).
thf(258,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/sandbox2/benchmark/theBenchmark.p',cls_hext__objD_0) ).
thf(1073,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)],[258]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).
thf(614,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)],[67]) ).
thf(407,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
!= ( c_Option_Ooption_ONone @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(1437,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)],[407]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__None__iff_0) ).
thf(1486,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)],[427]) ).
thf(293,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1158,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)],[293]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).
thf(582,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)],[55]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_0) ).
thf(762,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)],[131]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',cls_empty__map__add_0) ).
thf(1041,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)],[244]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',cls_map__of__Cons__code_I2_J_1) ).
thf(861,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)],[171]) ).
thf(20,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(500,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',cls_oconf__hext_0) ).
thf(1164,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)],[295]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(715,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)],[112]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_0) ).
thf(472,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)],[7]) ).
thf(362,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1327,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)],[362]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ( c_Option_Othe @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(1260,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)],[332]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_apfst__eq__conv_0) ).
thf(1078,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)],[260]) ).
thf(402,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/sandbox2/benchmark/theBenchmark.p',cls_Val_0) ).
thf(1426,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)],[402]) ).
thf(367,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/sandbox2/benchmark/theBenchmark.p',cls_restrict__out_0) ).
thf(1342,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)],[367]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',cls_hext__typeof__mono_0) ).
thf(913,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)],[192]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(538,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)],[38]) ).
thf(372,axiom,
( ( c_Objects_Otypeof__h @ v_ha____ @ v_v____ )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ v_Tv____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typeofv_0) ).
thf(1354,plain,
( ( c_Objects_Otypeof__h @ v_ha____ @ v_v____ )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ v_Tv____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(434,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/sandbox2/benchmark/theBenchmark.p',cls_dom__empty_0) ).
thf(1507,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)],[434]) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',cls_split__paired__All_0) ).
thf(1222,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)],[318]) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__empty_0) ).
thf(1196,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)],[308]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict__conv_0) ).
thf(898,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)],[186]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_ha_0) ).
thf(1391,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)],[387]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(782,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)],[138]) ).
thf(109,axiom,
! [A: $i] : ( c_Objects_Ohext @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__refl_0) ).
thf(709,plain,
! [A: $i] : ( c_Objects_Ohext @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__comp_0) ).
thf(885,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)],[180]) ).
thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_prod_Osplit__asm_0) ).
thf(1359,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)],[374]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).
thf(565,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)],[49]) ).
thf(444,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/sandbox2/benchmark/theBenchmark.p',cls_zip__Cons__Cons_0) ).
thf(1529,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)],[444]) ).
thf(334,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__empty_I2_J_0) ).
thf(1265,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)],[334]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__empty__conv_0) ).
thf(1254,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)],[330]) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1243,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)],[326]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
thf(1127,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)],[280]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).
thf(570,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)],[51]) ).
thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_swap__def_0) ).
thf(1298,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)],[349]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(785,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)],[139]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',cls_override__on__apply__notin_0) ).
thf(1330,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)],[363]) ).
thf(360,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/sandbox2/benchmark/theBenchmark.p',cls_empty__upd__none_0) ).
thf(1323,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)],[360]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(802,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)],[146]) ).
thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_curryI_0) ).
thf(1279,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)],[341]) ).
thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed2_0) ).
thf(1462,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)],[417]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(702,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)],[106]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__compose_0) ).
thf(751,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)],[126]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1191,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)],[306]) ).
thf(452,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/sandbox2/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
thf(1545,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)],[452]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',cls_setsum__reindex__id_0) ).
thf(559,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)],[47]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',cls_upd__None__map__le_0) ).
thf(853,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)],[167]) ).
thf(383,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1379,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)],[383]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1013,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)],[233]) ).
thf(391,axiom,
! [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_Objects_Oinit__fields @ D ) ) @ E )
| ~ ( c_TypeRel_OFields @ A @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_oconf__init__fields_0) ).
thf(1398,plain,
! [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_Objects_Oinit__fields @ D ) ) @ E )
| ~ ( c_TypeRel_OFields @ A @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',cls_Pair__scomp_0) ).
thf(1100,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)],[269]) ).
thf(322,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/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1232,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)],[322]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(969,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)],[214]) ).
thf(63,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(606,plain,
class_HOL_Ominus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(369,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).
thf(1347,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)],[369]) ).
thf(428,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/sandbox2/benchmark/theBenchmark.p',cls_hconf__new_0) ).
thf(1489,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)],[428]) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_1) ).
thf(924,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)],[196]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1450,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)],[412]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(82,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(646,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1151,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)],[290]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(806,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)],[148]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_FAss_0) ).
thf(966,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)],[213]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_Pair__fst__snd__eq_0) ).
thf(480,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)],[10]) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_option_Orecs_I2_J_0) ).
thf(1302,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)],[351]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_scomp__def_0) ).
thf(756,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)],[128]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__swap__iff_0) ).
thf(485,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)],[12]) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1136,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)],[283]) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_hconfD_0) ).
thf(1020,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)],[236]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(302,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/sandbox2/benchmark/theBenchmark.p',cls_prod__case__beta_0) ).
thf(1183,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)],[302]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).
thf(1283,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)],[343]) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_fst__eqD_0) ).
thf(1377,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)],[382]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__simps_I2_J_0) ).
thf(1215,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)],[315]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',cls_apfst__compose_0) ).
thf(877,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)],[177]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(956,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)],[209]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__upds_0) ).
thf(660,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)],[88]) ).
thf(226,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/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(998,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)],[226]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(1405,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)],[394]) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',cls_option_Ocase__cong_1) ).
thf(1201,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)],[310]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__upd_0) ).
thf(1521,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)],[440]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_3) ).
thf(507,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)],[24]) ).
thf(368,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(1345,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)],[368]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',cls_elem__set_0) ).
thf(988,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)],[222]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).
thf(1104,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)],[271]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_splitD_0) ).
thf(849,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)],[165]) ).
thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_is__none__def__raw_0) ).
thf(942,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)],[203]) ).
thf(291,axiom,
! [F: $i,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 @ E @ F )
| ~ ( c_TypeRel_Owiden @ D @ C @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__def_2) ).
thf(1153,plain,
! [F: $i,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 @ E @ F )
| ~ ( c_TypeRel_Owiden @ D @ C @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).
thf(810,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)],[150]) ).
thf(247,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1047,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)],[247]) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed1_0) ).
thf(1274,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)],[339]) ).
thf(184,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(894,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)],[184]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',cls_snd__apfst_0) ).
thf(1091,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)],[265]) ).
thf(439,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_5) ).
thf(1519,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)],[439]) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).
thf(1174,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)],[299]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',cls_preallocated__new_0) ).
thf(820,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)],[154]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',cls_option_Ocase__cong_0) ).
thf(815,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)],[152]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).
thf(693,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)],[102]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',cls_option_Orecs_I1_J_0) ).
thf(630,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)],[75]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(788,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)],[140]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_1) ).
thf(1370,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)],[379]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(916,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)],[193]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1032,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)],[240]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(879,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)],[178]) ).
thf(415,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/sandbox2/benchmark/theBenchmark.p',cls_ran__map__upd_0) ).
thf(1457,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)],[415]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__swap__iff_1) ).
thf(461,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)],[3]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',cls_prod__eqI_0) ).
thf(682,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)],[97]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_ONone @ B ) )
| ~ ( hBOOL @ ( c_Option_Ois__none @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__none__def_0) ).
thf(551,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)],[43]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1281,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)],[342]) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_dom__minus_0) ).
thf(974,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)],[216]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_1) ).
thf(522,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)],[30]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_scomp__Pair_0) ).
thf(830,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)],[158]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_fst__conv_0) ).
thf(1291,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)],[346]) ).
thf(110,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_Progress_OWTrt_H @ D @ A @ E @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I3_J_0) ).
thf(710,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_Progress_OWTrt_H @ D @ A @ E @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1350,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)],[370]) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1270,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)],[337]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(650,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)],[84]) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',cls_snd__apsnd_0) ).
thf(1375,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)],[381]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__apfst__commute_0) ).
thf(1064,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)],[254]) ).
thf(431,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/sandbox2/benchmark/theBenchmark.p',cls_the__inv__into__comp_0) ).
thf(1498,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)],[431]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1096,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_0) ).
thf(1006,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)],[230]) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).
thf(1138,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)],[284]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).
thf(593,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)],[58]) ).
thf(174,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/sandbox2/benchmark/theBenchmark.p',cls_split__beta_0) ).
thf(869,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)],[174]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] : ( c_TypeRel_Owiden @ A @ B @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] : ( c_TypeRel_Owiden @ A @ B @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__map__add__dom_0) ).
thf(1118,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)],[276]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(499,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)],[19]) ).
thf(390,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1397,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)],[390]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).
thf(697,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)],[104]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__o__empty_0) ).
thf(1089,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)],[264]) ).
thf(449,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem__set_1) ).
thf(1541,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)],[449]) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).
thf(874,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)],[176]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1143,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)],[286]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',cls_prod_Ocases_0) ).
thf(1534,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)],[446]) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(1017,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)],[235]) ).
thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_curry__split_0) ).
thf(1361,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)],[375]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).
thf(669,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)],[92]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',cls_option_Ocase__cong_3) ).
thf(901,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)],[187]) ).
thf(401,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__Some_0) ).
thf(1424,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)],[401]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Product__Type_Oprod_Oprod__case @ A @ B @ C )
= ( c_split @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_prod__case__split_0) ).
thf(642,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)],[80]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( ( c_Value_Oval_OAddr @ A )
!= ( c_Value_Oval_OAddr @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I3_J_0) ).
thf(526,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)],[32]) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(637,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)],[78]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',cls_swap__nilpotent_0) ).
thf(489,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)],[14]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',cls_set__empty__eq_1) ).
thf(1207,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)],[312]) ).
thf(399,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).
thf(1419,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)],[399]) ).
thf(44,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(554,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_3) ).
thf(753,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)],[127]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
thf(679,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)],[95]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__empty_I1_J_0) ).
thf(1039,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)],[243]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
thf(647,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)],[83]) ).
thf(413,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_4) ).
thf(1451,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)],[413]) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__eq__conv_0) ).
thf(1382,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)],[384]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(654,plain,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1,negated_conjecture,
~ ( c_Conform_Ooconf @ v_P @ v_ha____ @ ( 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_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(457,plain,
~ ( c_Conform_Ooconf @ v_P @ v_ha____ @ ( 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_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(137,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(779,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)],[137]) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',cls_prod_Osplit_0) ).
thf(1525,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)],[442]) ).
thf(72,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_TypeRel_Owiden @ A @ B @ C @ D )
| ~ ( c_TypeRel_Owiden @ A @ E @ C @ D )
| ~ ( c_TypeRel_Owiden @ A @ B @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__trans_0) ).
thf(622,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_TypeRel_Owiden @ A @ B @ C @ D )
| ~ ( c_TypeRel_Owiden @ A @ E @ C @ D )
| ~ ( c_TypeRel_Owiden @ A @ B @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_map__of__filter__in_0) ).
thf(837,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)],[161]) ).
thf(27,axiom,
! [A: $i] :
( ( c_Value_Oval_OAddr @ A )
!= c_Value_Oval_OUnit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I11_J_0) ).
thf(515,plain,
! [A: $i] :
( ( c_Value_Oval_OAddr @ A )
!= c_Value_Oval_OUnit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(424,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/sandbox2/benchmark/theBenchmark.p',cls_preallocated__upd__obj_0) ).
thf(1478,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)],[424]) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__map__add__dom_1) ).
thf(984,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)],[220]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_curryD_0) ).
thf(911,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)],[191]) ).
thf(50,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
thf(569,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',cls_splitI_0) ).
thf(1429,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)],[404]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
thf(503,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)],[22]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_0) ).
thf(1393,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)],[388]) ).
thf(364,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/sandbox2/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1333,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)],[364]) ).
thf(406,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/sandbox2/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).
thf(1434,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)],[406]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(792,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)],[142]) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_conf__upd__obj_0) ).
thf(1086,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)],[263]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',cls_comp__swap_0) ).
thf(541,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)],[39]) ).
thf(344,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/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(1286,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)],[344]) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__insert_0) ).
thf(1187,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)],[304]) ).
thf(437,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Option_Ooption_OSome @ A ) @ B @ A @ ( tc_Option_Ooption @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__Some_0) ).
thf(1515,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)],[437]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_2) ).
thf(1026,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)],[238]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).
thf(530,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)],[33]) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1185,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)],[303]) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(926,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)],[197]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_restrict__in_0) ).
thf(765,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)],[132]) ).
thf(250,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1054,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)],[250]) ).
thf(419,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/sandbox2/benchmark/theBenchmark.p',cls_snd__eqD_0) ).
thf(1466,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)],[419]) ).
thf(46,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(558,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).
thf(773,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)],[135]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_5) ).
thf(794,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)],[143]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(586,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)],[56]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Exceptions_Opreallocated @ A )
| ~ ( c_Conform_Ohconf @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hconf__def_1) ).
thf(662,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)],[89]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_pair__collapse_0) ).
thf(718,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)],[113]) ).
thf(189,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_Conform_Osko__Conform__Xconf__def__1__1 @ C @ D @ A @ B @ E ) ) )
| ~ ( c_Conform_Oconf @ C @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__def_0) ).
thf(906,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_Conform_Osko__Conform__Xconf__def__1__1 @ C @ D @ A @ B @ E ) ) )
| ~ ( c_Conform_Oconf @ C @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_wt_0) ).
thf(1273,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)],[338]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_domIff_1) ).
thf(1548,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)],[453]) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(856,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)],[169]) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(745,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)],[124]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__imp__upd__le_0) ).
thf(733,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)],[119]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(601,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)],[61]) ).
thf(329,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/sandbox2/benchmark/theBenchmark.p',cls_map__upds__apply__nontin_0) ).
thf(1251,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)],[329]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
| ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).
thf(618,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
| ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__def__raw_0) ).
thf(513,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)],[26]) ).
thf(288,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/sandbox2/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).
thf(1146,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)],[288]) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',cls_WTrtVal_0) ).
thf(843,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)],[163]) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1388,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)],[386]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__conv_0) ).
thf(743,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)],[123]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',cls_swap__triple_0) ).
thf(579,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)],[54]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_1) ).
thf(1124,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)],[279]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_fst__apsnd_0) ).
thf(904,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)],[188]) ).
thf(156,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(826,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)],[156]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(577,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)],[53]) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).
thf(958,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)],[210]) ).
thf(393,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/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAccRed_0) ).
thf(1403,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)],[393]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_0) ).
thf(1226,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)],[320]) ).
thf(41,axiom,
! [A: $i] :
( c_Value_Oval_OUnit
!= ( c_Value_Oval_OAddr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I10_J_0) ).
thf(545,plain,
! [A: $i] :
( c_Value_Oval_OUnit
!= ( c_Value_Oval_OAddr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',cls_map__of__zip__upd_0) ).
thf(936,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)],[201]) ).
thf(355,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/sandbox2/benchmark/theBenchmark.p',cls_apfst__conv_0) ).
thf(1312,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)],[355]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).
thf(611,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)],[66]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).
thf(466,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)],[5]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).
thf(704,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)],[107]) ).
thf(319,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/sandbox2/benchmark/theBenchmark.p',cls_inv__into__into_0) ).
thf(1224,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)],[319]) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_hext__def_0) ).
thf(1356,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)],[373]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).
thf(672,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)],[93]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(713,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)],[111]) ).
thf(18,axiom,
! [A: $i] : ( hBOOL @ ( c_Option_Ois__none @ ( c_Option_Ooption_ONone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__none__def_1) ).
thf(498,plain,
! [A: $i] : ( hBOOL @ ( c_Option_Ois__none @ ( c_Option_Ooption_ONone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).
thf(1058,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)],[252]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).
thf(1107,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)],[272]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_4) ).
thf(919,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)],[194]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1464,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)],[418]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__None__iff_3) ).
thf(947,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)],[205]) ).
thf(307,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/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1194,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)],[307]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1209,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)],[313]) ).
thf(232,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/sandbox2/benchmark/theBenchmark.p',cls_dom__const_0) ).
thf(1011,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)],[232]) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(996,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)],[225]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(1492,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)],[429]) ).
thf(450,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__empty_0) ).
thf(1542,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)],[450]) ).
thf(287,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1144,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)],[287]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_7) ).
thf(737,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)],[121]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
| ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).
thf(599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
| ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1307,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)],[353]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',cls_map__upds__twist_0) ).
thf(979,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)],[218]) ).
thf(62,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_TypeRel_OFields @ A @ B @ ( c_TypeRel_Osko__TypeRel__Xhas__field__def__1__1 @ B @ C @ D @ A @ E @ F ) @ F )
| ~ ( c_TypeRel_Ohas__field @ A @ B @ D @ E @ C @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has__field__def_0) ).
thf(604,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_TypeRel_OFields @ A @ B @ ( c_TypeRel_Osko__TypeRel__Xhas__field__def__1__1 @ B @ C @ D @ A @ E @ F ) @ F )
| ~ ( c_TypeRel_Ohas__field @ A @ B @ D @ E @ C @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(96,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(681,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(395,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/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_0) ).
thf(1408,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)],[395]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).
thf(509,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)],[25]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1043,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)],[245]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(616,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)],[68]) ).
thf(278,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_Option_Ois__none @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__none__code_I2_J_0) ).
thf(1122,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)],[278]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
thf(890,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)],[182]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).
thf(477,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)],[9]) ).
thf(421,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/sandbox2/benchmark/theBenchmark.p',cls_hext__new_0) ).
thf(1471,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)],[421]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
thf(494,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)],[16]) ).
thf(456,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/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Cons_0) ).
thf(1557,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)],[456]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_hext__trans_0) ).
thf(535,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)],[36]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(621,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)],[71]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( c_Exceptions_Opreallocated @ A )
| ~ ( c_Objects_Ohext @ B @ A )
| ~ ( c_Exceptions_Opreallocated @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preallocated__hext_0) ).
thf(483,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)],[11]) ).
thf(361,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).
thf(1325,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)],[361]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1029,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)],[239]) ).
thf(289,axiom,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(1149,plain,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).
thf(626,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)],[74]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1460,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)],[416]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',cls_snd__conv_0) ).
thf(1293,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)],[347]) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).
thf(1177,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)],[300]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(758,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)],[129]) ).
thf(366,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/sandbox2/benchmark/theBenchmark.p',cls_oconf__new_0) ).
thf(1339,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)],[366]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_1) ).
thf(799,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)],[145]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',cls_mem__splitI_0) ).
thf(726,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)],[116]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oswap @ A @ A @ B @ C @ D )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_swap__self_0) ).
thf(700,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)],[105]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(520,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)],[29]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(932,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)],[199]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1061,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)],[253]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1198,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)],[309]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1474,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)],[422]) ).
thf(234,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1015,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)],[234]) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',cls_ospec_0) ).
thf(986,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)],[221]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',cls_o__inv__o__cancel_0) ).
thf(1113,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)],[274]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).
thf(1000,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)],[227]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Oid @ B ) @ B @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(505,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)],[23]) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(922,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)],[195]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__imp__inj__on__swap_0) ).
thf(658,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)],[87]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_fequal @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(685,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_fequal @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1171,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)],[298]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(768,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)],[133]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(827,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)],[157]) ).
thf(77,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(636,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(695,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)],[103]) ).
thf(327,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_0) ).
thf(1245,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)],[327]) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',cls_oconf__fupd_0) ).
thf(1066,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)],[255]) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1445,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)],[410]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_inv__id_0) ).
thf(851,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)],[166]) ).
thf(270,axiom,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1102,plain,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',cls_domI_0) ).
thf(1034,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)],[241]) ).
thf(352,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(1304,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)],[352]) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1166,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)],[296]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(589,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)],[57]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',cls_setprod__reindex__cong_0) ).
thf(548,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)],[42]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(487,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)],[13]) ).
thf(435,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__simps_I1_J_0) ).
thf(1509,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)],[435]) ).
thf(261,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/sandbox2/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).
thf(1081,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)],[261]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_FAcc_0) ).
thf(939,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)],[202]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).
thf(823,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)],[155]) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',cls_insert__dom_0) ).
thf(1551,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)],[454]) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',cls_inv__into__comp_0) ).
thf(1049,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)],[248]) ).
thf(397,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ ( c_TypeRel_Osko__TypeRel__Xhas__field__def__1__1 @ A @ B @ C @ D @ E @ F ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ tc_Type_Oty ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) @ B ) )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ E ) )
| ~ ( c_TypeRel_Ohas__field @ D @ A @ C @ E @ B @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has__field__def_1) ).
thf(1413,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ ( c_TypeRel_Osko__TypeRel__Xhas__field__def__1__1 @ A @ B @ C @ D @ E @ F ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ tc_Type_Oty ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) @ B ) )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ E ) )
| ~ ( c_TypeRel_Ohas__field @ D @ A @ C @ E @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_split__curry_0) ).
thf(1076,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)],[259]) ).
thf(34,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_fequal @ A @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(531,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_fequal @ A @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).
thf(944,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)],[204]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).
thf(776,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)],[136]) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1003,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)],[228]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_3) ).
thf(1070,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)],[257]) ).
thf(292,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/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1156,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)],[292]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_0) ).
thf(887,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)],[181]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__None__iff_1) ).
thf(971,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)],[215]) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',cls_conjI__realizer_1) ).
thf(954,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)],[208]) ).
thf(335,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/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1267,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)],[335]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',cls_ranI_0) ).
thf(1531,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)],[445]) ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).
thf(1484,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)],[426]) ).
thf(268,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/sandbox2/benchmark/theBenchmark.p',cls_exI__realizer_0) ).
thf(1098,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)],[268]) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(993,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)],[224]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(690,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)],[100]) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1516,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)],[438]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).
thf(1400,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)],[392]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).
thf(707,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)],[108]) ).
thf(350,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__def_0) ).
thf(1300,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)],[350]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__eq__conv_1) ).
thf(840,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)],[162]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).
thf(463,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)],[4]) ).
thf(358,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/sandbox2/benchmark/theBenchmark.p',cls_image__map__upd_0) ).
thf(1317,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)],[358]) ).
thf(6,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Conform_Oconf @ A @ B @ C @ D @ E )
| ~ ( c_TypeRel_Owiden @ A @ F @ D @ E )
| ~ ( c_Conform_Oconf @ A @ B @ C @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__widen_0) ).
thf(470,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Conform_Oconf @ A @ B @ C @ D @ E )
| ~ ( c_TypeRel_Owiden @ A @ F @ D @ E )
| ~ ( c_Conform_Oconf @ A @ B @ C @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1130,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)],[281]) ).
thf(316,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(1218,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)],[316]) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).
thf(1336,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)],[365]) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_0) ).
thf(1220,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)],[317]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).
thf(1262,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)],[333]) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',cls_conjI__realizer_0) ).
thf(1235,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)],[323]) ).
thf(448,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/sandbox2/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).
thf(1538,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)],[448]) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_typeof__conf_0) ).
thf(951,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)],[207]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',cls_fst__apfst_0) ).
thf(808,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)],[149]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1543,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)],[451]) ).
thf(331,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/sandbox2/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).
thf(1257,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)],[331]) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1052,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)],[249]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',cls_override__on__apply__in_0) ).
thf(864,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)],[172]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',cls_override__on__emptyset_0) ).
thf(1427,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)],[403]) ).
thf(433,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ A @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ tc_Type_Oty ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
!= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ D ) )
| ~ ( c_TypeRel_OFields @ E @ F @ A @ G )
| ( c_TypeRel_Ohas__field @ E @ F @ B @ D @ C @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has__field__def_2) ).
thf(1504,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ A @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ tc_Type_Oty ) @ ( hAPP @ ( hAPP @ ( c_Pair @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) )
!= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Type_Oty ) @ D ) )
| ~ ( c_TypeRel_OFields @ E @ F @ A @ G )
| ( c_TypeRel_Ohas__field @ E @ F @ B @ D @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(170,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__o__map__upd_0) ).
thf(859,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)],[170]) ).
thf(285,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/sandbox2/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
thf(1141,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)],[285]) ).
thf(447,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/sandbox2/benchmark/theBenchmark.p',cls_surjective__pairing_0) ).
thf(1536,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)],[447]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Product__Type_Ointernal__split @ A @ B @ C )
= ( c_split @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_internal__split__def_0) ).
thf(656,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)],[86]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(1023,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)],[237]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1240,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)],[325]) ).
thf(223,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(991,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)],[223]) ).
thf(400,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/sandbox2/benchmark/theBenchmark.p',cls_oconf__upd__obj_0) ).
thf(1421,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)],[400]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',cls_hext__upd__obj_0) ).
thf(1180,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)],[301]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(688,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)],[99]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',cls_swap__commute_0) ).
thf(524,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)],[31]) ).
thf(345,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd_0) ).
thf(1289,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)],[345]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',cls_ospec_1) ).
thf(771,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)],[134]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(262,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/sandbox2/benchmark/theBenchmark.p',cls_scomp__apply_0) ).
thf(1084,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)],[262]) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1448,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)],[411]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_1) ).
thf(1189,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)],[305]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(1276,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)],[340]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',cls_the__inv__into__f__eq_0) ).
thf(963,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)],[212]) ).
thf(423,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(1476,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)],[423]) ).
thf(425,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/sandbox2/benchmark/theBenchmark.p',cls_apfst__eq__conv_1) ).
thf(1481,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)],[425]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Expr_Oexp_OVal @ A @ B )
!= ( c_Expr_Oexp_OVal @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).
thf(632,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)],[76]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__comp_0) ).
thf(1523,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)],[441]) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',cls_ran__empty_0) ).
thf(961,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)],[211]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_override__on__upd__lemma_0) ).
thf(813,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)],[151]) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1385,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)],[385]) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',cls_split__paired__Ex_1) ).
thf(896,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)],[185]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(748,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)],[125]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1212,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)],[314]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__Some__iff_2) ).
thf(832,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)],[159]) ).
thf(354,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/sandbox2/benchmark/theBenchmark.p',cls_inj__iff_0) ).
thf(1309,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)],[354]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).
thf(1442,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)],[409]) ).
thf(246,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__empty_0) ).
thf(1045,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)],[246]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',cls_hconf__upd__obj_0) ).
thf(1161,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)],[294]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_Option_Oset_Osimps_I2_J_0) ).
thf(1440,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)],[408]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedFAss_0) ).
thf(929,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)],[198]) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__None_0) ).
thf(1116,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)],[275]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_2) ).
thf(1133,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)],[282]) ).
thf(70,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(620,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(436,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).
thf(1512,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)],[436]) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',cls_map__of__zip__is__None_0) ).
thf(1229,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)],[321]) ).
thf(389,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/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1395,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)],[389]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(818,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)],[153]) ).
thf(168,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/sandbox2/benchmark/theBenchmark.p',cls_map__of_Osimps_I2_J_0) ).
thf(854,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)],[168]) ).
thf(443,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/sandbox2/benchmark/theBenchmark.p',cls_apfst__def_0) ).
thf(1527,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)],[443]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(867,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)],[173]) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_prod__caseI_0) ).
thf(735,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)],[120]) ).
thf(206,axiom,
c_Conform_Ohconf @ v_P @ v_ha____ @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hconf_0) ).
thf(950,plain,
c_Conform_Ohconf @ v_P @ v_ha____ @ ( 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)],[206]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).
thf(835,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)],[160]) ).
thf(328,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1248,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)],[328]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(790,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)],[141]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',cls_inv__f__f_0) ).
thf(1495,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)],[430]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(474,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)],[8]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(532,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)],[35]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(720,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)],[114]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__is__None_0) ).
thf(796,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)],[144]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I5_J_0) ).
thf(1363,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)],[376]) ).
thf(356,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1314,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)],[356]) ).
thf(251,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/sandbox2/benchmark/theBenchmark.p',cls_apsnd__apfst_0) ).
thf(1056,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)],[251]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).
thf(664,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)],[90]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',cls_split__comp_0) ).
thf(1352,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)],[371]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',cls_apfst__apsnd_0) ).
thf(1268,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)],[336]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',cls_setprod__reindex_0) ).
thf(596,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)],[59]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',cls_conf__hext_0) ).
thf(644,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)],[81]) ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_TypeRel_Owiden @ A @ ( c_Conform_Osko__Conform__Xconf__def__1__1 @ A @ B @ C @ D @ E ) @ B @ E )
| ~ ( c_Conform_Oconf @ A @ C @ D @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__def_1) ).
thf(459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_TypeRel_Owiden @ A @ ( c_Conform_Osko__Conform__Xconf__def__1__1 @ A @ B @ C @ D @ E ) @ B @ E )
| ~ ( c_Conform_Oconf @ A @ C @ D @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(723,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)],[115]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(691,plain,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_6) ).
thf(871,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)],[175]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',cls_internal__split__conv_0) ).
thf(1120,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)],[277]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(501,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)],[21]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
thf(607,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)],[64]) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).
thf(1093,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)],[266]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_map__le__upds_0) ).
thf(624,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)],[73]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',cls_curry__conv_0) ).
thf(728,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)],[117]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',cls_conf__upd__obj_1) ).
thf(740,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)],[122]) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_splitD_H_0) ).
thf(982,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)],[219]) ).
thf(405,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/sandbox2/benchmark/theBenchmark.p',cls_inj__iff_1) ).
thf(1431,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)],[405]) ).
thf(359,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/sandbox2/benchmark/theBenchmark.p',cls_map__of__zip__is__None_1) ).
thf(1320,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)],[359]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
!= ( c_Option_Ooption_ONone @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(1367,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)],[378]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_eval__hext_0) ).
thf(1009,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)],[231]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).
thf(543,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)],[40]) ).
thf(242,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/sandbox2/benchmark/theBenchmark.p',cls_prod__fun_0) ).
thf(1037,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)],[242]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_map__of__zip__is__Some_1) ).
thf(1416,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)],[398]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',cls_setprod__reindex__id_0) ).
thf(639,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)],[79]) ).
thf(94,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_TypeRel_OFields @ C @ D @ A @ E )
| ~ ( c_TypeRel_OFields @ C @ D @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has__fields__fun_0) ).
thf(676,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_TypeRel_OFields @ C @ D @ A @ E )
| ~ ( c_TypeRel_OFields @ C @ D @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).
thf(491,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)],[15]) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1204,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)],[311]) ).
thf(420,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1468,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)],[420]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__iff_2) ).
thf(496,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)],[17]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',cls_set__empty__eq_0) ).
thf(882,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)],[179]) ).
thf(28363,plain,
$false,
inference(cvc4,[status(thm)],[1501,1411,1454,909,893,518,555,1168,760,1237,846,666,1295,1554,1110,977,1005,730,1068,1073,614,1437,1486,1158,582,762,1041,861,500,1164,715,472,1327,1260,1078,1426,1342,913,538,1354,1507,1222,1196,898,1391,782,709,885,1359,565,1529,1265,1254,1243,1127,570,1298,785,1330,1323,802,1279,1462,702,751,934,1191,1545,559,853,1379,1013,1398,1100,1232,969,606,1347,1489,924,1450,1373,646,1151,806,966,480,1302,756,485,1136,1020,574,1183,1283,1377,1215,877,956,660,998,1405,1201,1521,507,1345,988,1104,849,942,1153,810,1047,1274,894,1091,1519,1174,820,815,693,630,788,1370,916,1032,1365,879,1457,461,682,551,1281,974,522,830,1291,710,1350,1270,650,1375,1064,1498,1096,1006,1138,593,869,610,1118,499,1397,697,1089,1541,874,1143,1534,1017,1361,537,669,901,1424,642,526,637,489,1207,1419,554,753,679,1039,647,1451,1382,654,457,779,1525,622,837,515,1478,984,911,569,1429,503,1393,1333,1434,792,1086,541,1286,1187,1515,1026,530,1185,926,765,1054,1466,558,773,794,586,662,718,906,1273,1548,856,745,733,601,1251,618,513,1146,843,1388,743,579,1124,562,904,826,577,958,1403,1226,545,936,1312,611,466,704,1224,1356,672,713,498,1058,1107,919,804,1464,947,1194,1209,1011,996,1492,1542,1144,737,599,1307,979,604,681,1408,509,1043,616,1122,890,477,1471,494,1557,535,621,483,1325,1029,1149,626,1460,1293,1177,758,1339,799,726,700,520,932,1061,1198,1474,1015,986,1113,1000,505,922,658,685,1171,768,827,636,695,1245,1066,1445,851,1102,1034,1304,1166,589,548,487,1509,1081,939,823,1551,1049,1413,1076,531,944,776,1003,1070,1156,887,971,954,1267,1531,1484,1098,993,690,1516,1400,707,1300,840,463,1317,470,1130,1218,1336,1220,1262,1235,1538,951,808,1543,1257,1052,864,1427,1504,859,1141,1536,656,1023,1240,991,1421,1180,688,524,1289,771,1316,1084,1448,1189,1276,963,1476,1481,632,1523,961,813,1385,896,748,1212,832,1309,1442,1045,1161,1440,929,1116,1133,620,1512,1229,1395,818,854,1527,867,735,950,835,1248,790,1495,474,532,720,796,1363,1314,1056,664,1352,1268,596,644,459,723,691,871,1120,501,607,1093,624,728,740,982,1431,1320,1367,1009,543,1037,1416,639,676,491,1204,1468,496,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV919-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:49:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.12 % [INFO] Parsing done (240ms).
% 1.65/1.12 % [INFO] Running in sequential loop mode.
% 2.29/1.32 % [INFO] eprover registered as external prover.
% 2.29/1.32 % [INFO] cvc4 registered as external prover.
% 2.29/1.33 % [INFO] Scanning for conjecture ...
% 2.51/1.45 % [INFO] Found a conjecture and 455 axioms. Running axiom selection ...
% 3.11/1.57 % [INFO] Axiom selection finished. Selected 455 axioms (removed 0 axioms).
% 3.70/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 3.70/1.75 % [INFO] Type checking passed.
% 3.70/1.75 % [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 ...
% 83.11/20.55 % External prover 'cvc4' found a proof!
% 83.11/20.55 % [INFO] Killing All external provers ...
% 83.11/20.55 % Time passed: 20030ms (effective reasoning time: 19420ms)
% 83.11/20.55 % 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)>
% 83.11/20.55 % Axioms used in derivation (455): cls_inj__Some_0, cls_val_Osimps_I3_J_0, cls_restrict__map__to__empty_0, cls_set__empty__eq_1, cls_bot__fun__eq_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_has__field__def_1, cls_Diff__iff_2, cls_FAcc_0, cls_snd__conv_0, cls_image__constant_0, cls_inj__iff_1, cls_splitD_H_0, cls_internal__split__def_0, cls_snd__eqD_0, cls_apsnd__conv_0, cls_val_Osimps_I10_J_0, cls_split__comp_0, cls_map__add__None_2, cls_conf__def_2, cls_insertE_0, cls_id__o_0, cls_fun__upd__image_1, cls_inj__on__image__iff_4, cls_swap__def_0, cls_ospec_1, cls_the__inv__f__f_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_inv__into__comp_0, cls_map__upd__Some__unfold_4, cls_eval__cases_I1_J_1, cls_redp__redsp_OFAssRed1_0, cls_map__add__assoc_0, cls_set__ConsD_0, cls_exp_Osimps_I7_J_2, cls_insert__code_1, cls_map__le__trans_0, cls_fun__upd__apply_1, cls_has_0, cls_map__upd__Some__unfold_3, cls_restrict__fun__upd_0, cls_prod_Ocases_0, cls_Option_Oset_Osimps_I2_J_0, cls_COMBK__def_0, cls_list_Oinject_0, cls_oconf__new_0, cls_map__upds__apply__nontin_0, cls_map__of__Cons__code_I2_J_1, cls_map__comp__simps_I2_J_0, cls_insert__absorb_0, cls_apfst__def_0, cls_hconf__new_0, cls_hext__def_0, cls_option_Osimps_I2_J_0, cls_restrict__map__insert_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_map__le__iff__map__add__commute_0, cls_mem__def_1, cls_fun__upd__image_0, cls_map__comp__empty_I2_J_0, cls_split__curry_0, cls_exp_Osimps_I154_J_0, cls_insert__iff_1, cls_COMBI__def__raw_0, cls_filter__eq__ConsD_2, cls_swap__commute_0, cls_fun__upd__None__restrict_0, cls_K__record__comp_0, cls_dom__fun__upd_0, cls_splitI_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_typeof__conf_0, cls_map__add__Some__iff_3, cls_inj__image__mem__iff_0, cls_map__le__empty_0, cls_inj__on__image__iff_5, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I8_J_3, cls_filter_Osimps_I2_J_0, cls_is__none__def__raw_0, cls_map__of__zip__is__None_1, clsarity_fun__Orderings_Otop, cls_f__inv__into__f_0, cls_exI__realizer_0, cls_scomp__apply_0, cls_snd__apfst_0, cls_prod__case__split_0, cls_redp__redsp_ORedFAss_0, cls_empty__is__image_0, cls_rangeI_0, cls_conf__upd__obj_1, cls_widen__refl_0, cls_rev__image__eqI_0, cls_inj__on__insert_0, cls_Diff__UNIV_0, cls_map__upd__Some__unfold_0, cls_hext__upd__obj_0, cls_fun__upd__other_0, cls_is__none__code_I2_J_0, cls_override__on__upd__lemma_0, clsarity_fun__Orderings_Obot, cls_hext__trans_0, cls_f__the__inv__into__f_0, cls_map__le__def_0, cls_apsnd__compose_0, cls_insert__ident_0, cls_image__id_0, cls_redp__redsp_OFAssRed2_0, cls_ha_0, cls_has__fields__fun_0, cls_fst__eqD_0, cls_apfst__conv_0, 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cls_UNIV__not__empty_0, cls_the_Osimps_0, cls_exp_Osimps_I77_J_0, cls_map__add__dom__app__simps_I3_J_0, cls_doubleton__eq__iff_2, cls_map__upd__nonempty_0, cls_map__upds__twist_0, cls_hconf_0, cls_fun__upd__triv_0, clsarity_nat__Orderings_Obot, cls_setprod__reindex__id_0, cls_option_Orecs_I2_J_0, cls_apsnd__eq__conv_1, cls_inj__on__image__iff_2, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_ran__empty_0, cls_ex__in__conv_0, cls_exp_Osimps_I76_J_0, cls_option__map__None_0, cls_exp_Osimps_I8_J_2, cls_ranI_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_sub_0, cls_map__comp__Some__iff_2, cls_fun__upd__restrict__conv_0, cls_map__add__None_0, cls_conf__upd__obj_0, cls_option_Osplit_2, cls_oconf__init__fields_0, cls_comp__swap_0, cls_inj__on__image__iff_6, cls_Pair__scomp_0, cls_option_Osplit__asm_2, cls_map__of__filter__in_0, cls_Pair__fst__snd__eq_0, cls_not__Cons__self_0, cls_map__add__le__mapE_0, cls_image__empty_0, cls_dom__eq__singleton__conv_0, cls_DiffI_0, cls_inj__on__insert_1, cls_map__upd__triv_0, cls_map__upd__Some__unfold_1, cls_option_Osimps_I4_J_0, cls_map__add__upds_0, cls_exp_Osimps_I7_J_1, cls_dom__empty_0, cls_image__constant__conv_0, cls_inj__on__swap__iff_0, cls_insertI1_0, cls_split__case__cert_0, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_internal__split__conv_0, cls_FAss_0, cls_empty__not__insert_0, cls_insert__Diff1_0, cls_empty__map__add_0, cls_inv__id_0, cls_the__inv__into__comp_0, cls_fun__upd__twist_0, cls_image__ident_0, cls_Pair__eq_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_singletonE_0, cls_insert__Diff_0, cls_inj__on__empty_0, cls_elem__set_0, cls_image__iff_2, cls_insertCI_0, cls_fun__upd__apply_0, cls_wt_0, cls_image__set__diff_0, cls_dom__eq__singleton__conv_1, cls_inj__on__iff_0, 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cls_setsum__reindex__id_0, cls_map__upd__Some__unfold_2, cls_exp_Osimps_I8_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_map__comp__None__iff_1, cls_comm__monoid__add_Ononempty__iff_2, cls_map__add__dom__app__simps_I1_J_0, cls_singleton__inject_0, cls_conf__def_1, cls_inj__on__image__iff_3, cls_fun__upd__None__restrict_1, cls_empty__upd__none_0, cls_option_Osimps_I3_J_0, cls_option__map__o__empty_0, cls_inj__on__contraD_0, cls_inj__onD_0, cls_restrict__fun__upd_1, cls_Val_0, cls_the__inv__into__f__f_0, cls_mem__splitI_0, cls_option_Osplit__asm_5, cls_eval__hext_0, cls_setprod__reindex_0, cls_image__eqI_0, cls_conjI__realizer_1, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_inv__into__into_0, cls_insertCI_1, cls_option_Orecs_I1_J_0, cls_option_Osplit_0, cls_curry__conv_0, cls_doubleton__eq__iff_4, cls_insert__code_0, cls_map__add__find__right_0, cls_map__of_Osimps_I2_J_0, cls_inj__on__id2_0, cls_option__map__o__map__upd_0, cls_option_Osplit__asm_4, cls_conf__def_0, cls_domIff_1, cls_map__add__Some__iff_2, cls_DiffE_1, cls_dom__fun__upd_1, cls_apfst__compose_0, cls_map__of__zip__is__Some_1, cls_wt__wt_H_0, cls_inj__on__image__iff_0, cls_inv__f__f_0, cls_option_Ocase__cong_2, cls_map__le__iff__map__add__commute_1, cls_fun__upd__upd_0, cls_map__le__map__add_0, cls_map__of__zip__upd_0, cls_zip__Cons__Cons_0, cls_map__add__SomeD_1, cls_apsnd__def_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, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_COMBI__def_0, cls_exp_Osimps_I78_J_0, cls_restrict__map__empty_0, cls_option__map__Some_0, cls_image__is__empty_0, cls_filter_Osimps_I2_J_1, cls_inj__on__map__add__dom_1, cls_hext__new_0, cls_Pair__eq_1, cls_option_Osimps_I5_J_0, cls_imageI_0, cls_prod__case__beta_0, cls_map__comp__None__iff_2, cls_hext__typeof__mono_0, cls_image__compose_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_inv__into__f__eq_0, cls_fun__upd__comp_0, cls_exp_Osimps_I3_J_0, cls_map__add__None_1, clsarity_nat__HOL_Ominus, cls_o__assoc_0, cls_empty__Diff_0, cls_fun__upd__idem__iff_1, cls_oconf__hext_0, cls_image__inv__f__f_0, cls_fst__conv_0
% 83.11/20.55 % No. of inferences in proof: 913
% 83.11/20.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20030 ms resp. 19420 ms w/o parsing
% 83.86/20.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.86/20.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------