%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT162+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:22 AM UTC 2026
% Result : Theorem 23.85s 15.61s
% Output : Refutation 24.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 532
% Syntax : Number of formulae : 1066 ( 262 unt; 0 typ; 0 def)
% Number of atoms : 3062 ( 768 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 24518 ( 336 ~; 72 |; 253 &;22186 @)
% ( 121 <=>;1550 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 101 ( 99 usr; 24 con; 0-6 aty)
% Number of variables : 3130 ( 0 ^;3097 !; 33 ?;3130 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_member_decl,type,
c_member: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i ).
thf(c_If_decl,type,
c_If: $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(v_h_____decl,type,
v_h____: $i ).
thf(v_n_____decl,type,
v_n____: $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i ).
thf(v_P_____decl,type,
v_P____: $i ).
thf(v_e_____decl,type,
v_e____: $i ).
thf(c_fequal_decl,type,
c_fequal: $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
thf(v_c_____decl,type,
v_c____: $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
thf(c_Arrow__Order__Mirabelle_OProf_decl,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(c_List_Osplice_decl,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(class_Rings_Ozero__neq__one_decl,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $i > $o ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_decl,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(v_F_decl,type,
v_F: $i ).
thf(c_List_Olist_Olist__case_decl,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_decl,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_b_____decl,type,
v_b____: $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple_decl,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(class_Groups_Oordered__comm__monoid__add_decl,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Wellfounded_Olex__prod_decl,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(class_Groups_Ocancel__semigroup__add_decl,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(c_FuncSet_OPi_decl,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i ).
thf(v_Lab_____decl,type,
v_Lab____: $i ).
thf(v_Lba_____decl,type,
v_Lba____: $i ).
thf(c_Arrow__Order__Mirabelle_OLin_decl,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_decl,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(class_Groups_Olinordered__ab__group__add_decl,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_decl,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_List_Olist_Olist__size_decl,type,
c_List_Olist_Olist__size: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple__idem_decl,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_Hilbert__Choice_Oinv__into_decl,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_List_Omeasures_decl,type,
c_List_Omeasures: $i > $i > $i ).
thf(class_Rings_Oring__1_decl,type,
class_Rings_Oring__1: $i > $o ).
thf(c_Int_Oring__1__class_OInts_decl,type,
c_Int_Oring__1__class_OInts: $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(c_Wellfounded_Omlex__prod_decl,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Odictator_decl,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_decl,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $i > $o ).
thf(v_d_____decl,type,
v_d____: $i ).
thf(c_Wellfounded_Ofinite__psubset_decl,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_Nat_Onat_Onat__size_decl,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(c_Wellfounded_Omeasure_decl,type,
c_Wellfounded_Omeasure: $i > $i > $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(c_FunDef_Oin__rel_decl,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Recdef_Osame__fst_decl,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(892,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(532,axiom,
! [A: $i] : ( c_Arrow__Order__Mirabelle_OProf @ ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiProf) ).
thf(2630,plain,
! [A: $i] : ( c_Arrow__Order__Mirabelle_OProf @ ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(1501,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(2612,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(174,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(1168,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(242,axiom,
! [A: $i] :
( ( A @ c_Arrow__Order__Mirabelle_Ounanimity )
<=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(1454,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ c_Arrow__Order__Mirabelle_Ounanimity ) )
& ( ( A @ c_Arrow__Order__Mirabelle_Ounanimity )
=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(1729,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) )
& ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(194,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite ) )
<=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
thf(1237,plain,
! [A: $i] :
( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite ) ) )
& ( ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(2544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1549,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(2072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(323,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(1767,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(628,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(1031,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(394,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(2077,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(1158,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(2117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(683,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2062,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(741,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(2282,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
thf(655,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
thf(614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(136,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(1041,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(1750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(977,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(213,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1305,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(597,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(1078,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).
thf(1310,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(2448,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(913,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(2580,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(1954,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(538,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) )
& ( ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
thf(1497,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(429,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2195,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(307,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(1705,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
thf(797,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(458,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(2316,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(1275,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__lesseq) ).
thf(2141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
thf(1222,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(2360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Otop )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
thf(1196,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Otop )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(1243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(2020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(2010,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
thf(1921,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(1601,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2531,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(191,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(1228,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( C @ ( D @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(973,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( C @ ( D @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(1046,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(2400,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(1529,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(257,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(1518,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(202,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1265,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(719,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2269,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1330,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(1313,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(1992,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(1132,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(1055,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(59,axiom,
v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_n____ @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I3_J) ).
thf(724,plain,
v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_n____ @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(1760,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(299,axiom,
tc_HOL_Obool @ class_Orderings_Otop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(1660,plain,
tc_HOL_Obool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(587,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1545,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Olist_OCons ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(559,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_List_Olist_OCons ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(2403,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(1247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(114,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(969,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(1013,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1568,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(2024,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(1963,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(469,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(2388,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(1847,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(2456,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2237,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
thf(924,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(2616,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
thf(2324,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(2105,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
thf(591,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(1911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(25,axiom,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
thf(623,plain,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
thf(834,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
thf(1151,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(2291,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(1581,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
thf(1283,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(1109,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(1632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(502,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2508,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(2058,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(528,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2618,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(2424,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(38,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
thf(660,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(440,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(2242,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(399,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(2103,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1447,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
thf(956,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(2523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(507,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).
thf(2530,plain,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).
thf(1526,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
thf(2137,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2392,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(432,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(2204,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(1153,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(810,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(2047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(1,conjecture,
c_Arrow__Order__Mirabelle_OProf @ ( v_e____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Omkbot @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_e____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Oabove @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_n____ @ ( v_h____ @ ( c_fequal @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( v_e____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Omktop @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_n____ @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( c_Arrow__Order__Mirabelle_OProf @ ( v_e____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Omkbot @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_e____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Oabove @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_n____ @ ( v_h____ @ ( c_fequal @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( v_e____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Omktop @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_n____ @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(534,plain,
~ ( c_Arrow__Order__Mirabelle_OProf @ ( v_e____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Omkbot @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_e____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Oabove @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_n____ @ ( v_h____ @ ( c_fequal @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( v_e____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Omktop @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_n____ @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBS ) ) ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1636,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(1438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
thf(661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons ) ) @ ( E @ c_List_Osplice ) ) )
= ( A @ ( C @ ( E @ c_List_Osplice ) ) @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( E @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
thf(546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons ) ) @ ( E @ c_List_Osplice ) ) )
= ( A @ ( C @ ( E @ c_List_Osplice ) ) @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( E @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(793,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(1199,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(421,axiom,
v_Lab____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(2164,plain,
v_Lab____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons ) ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons ) ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons ) ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(1708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(1067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(2496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(2621,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(714,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(2382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite ) )
<=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
thf(2441,plain,
! [A: $i,B: $i] :
( ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite ) ) )
& ( ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(1900,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(517,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(2560,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(2249,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1255,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(820,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil )
!= ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
thf(630,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil )
!= ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(1824,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(729,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(1560,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(107,axiom,
( ( tc_HOL_Obool @ ( tc_Product__Type_Ounit @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Product__Type_Ounit @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
thf(952,plain,
( ( tc_HOL_Obool @ ( tc_Product__Type_Ounit @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Product__Type_Ounit @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_Set_Oimage ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_Set_Oimage ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(1938,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(1365,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(2477,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(211,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(1296,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Oring__char__0 )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
thf(1819,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Oring__char__0 )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(1836,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(179,axiom,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1195,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(52,axiom,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Fun_Oinj__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injh) ).
thf(710,plain,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Fun_Oinj__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(852,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
thf(1555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(2313,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(551,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(495,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(2492,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(1634,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
thf(2228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(348,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(1910,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
thf(2157,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1851,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(650,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(220,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(1328,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(1064,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
thf(980,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(2509,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(1540,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( D @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ ( D @ c_List_Olist_Olist__size ) ) @ ( B @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I2_J) ).
thf(857,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( D @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ ( D @ c_List_Olist_Olist__size ) ) @ ( B @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1360,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(1936,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(2498,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(1234,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
thf(1856,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(725,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
thf(1138,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(2537,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(249,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1493,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) )
<=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(642,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) ) )
& ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(2240,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) )
=> ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(1214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(16,axiom,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(590,plain,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(1155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(1419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice__Nil2) ).
thf(637,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1584,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
thf(1039,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( B @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
thf(837,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( B @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
<=> ! [D: $i] :
( ( D @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
thf(1297,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( D @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ! [D: $i] :
( ( D @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(738,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(1974,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(441,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2243,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1932,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(911,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
thf(2006,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(2566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(124,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(1002,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) )
=> ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(310,axiom,
~ ! [A: $i] :
( ( A @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1715,plain,
~ ! [A: $i] :
( ( A @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1720,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(321,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).
thf(1759,plain,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(485,axiom,
v_c____ != v_d____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096) ).
thf(2450,plain,
v_c____ != v_d____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1588,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(1099,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(168,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1150,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(1249,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(2465,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
thf(1050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(513,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(2546,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(382,axiom,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(2043,plain,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Oring__char__0 )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
thf(1695,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Oring__char__0 )
=> ( ( B @ c_Int_Oring__1__class_OInts @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(37,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(657,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(1187,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ( ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2408,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(2189,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(926,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
thf(1814,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(1086,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(309,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(1712,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(338,axiom,
tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_e____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_d____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dist) ).
thf(1846,plain,
tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_e____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_d____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(393,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(2076,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( E @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( D @ ( B @ ( E @ c_COMBB ) ) ) @ hAPP ) @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
thf(1170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( E @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( D @ ( B @ ( E @ c_COMBB ) ) ) @ hAPP ) @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1286,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(2368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(244,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(1466,plain,
c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
thf(1071,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B != A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(1135,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B != A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(1146,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(470,axiom,
c_Arrow__Order__Mirabelle_OProf @ ( v_P____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
thf(2391,plain,
c_Arrow__Order__Mirabelle_OProf @ ( v_P____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
thf(1273,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ocard ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(1747,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ocard ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
thf(2028,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(573,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
thf(965,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(1251,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i] :
~ ( tc_Nat_Onat @ ( C @ tc_fun ) @ c_List_Olist_ONil @ ( C @ c_List_Omeasures ) @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
thf(2413,plain,
! [A: $i,B: $i,C: $i] :
~ ( tc_Nat_Onat @ ( C @ tc_fun ) @ c_List_Olist_ONil @ ( C @ c_List_Omeasures ) @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1959,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(1103,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(351,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(1916,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(287,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(1615,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).
thf(2489,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(1752,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(1929,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(2568,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(579,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( A
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ c_Groups_Oone__class_Oone )
= A ) )
& ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(229,axiom,
? [A: $i] :
( ( v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ! [B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ @ ( v_Lab____ @ ( B @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096) ).
thf(1403,plain,
? [A: $i] :
( ( v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ! [B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ @ ( v_Lab____ @ ( B @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(1520,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(159,axiom,
~ ! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ @ ( v_Lab____ @ ( B @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1124,plain,
~ ! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ @ ( v_Lab____ @ ( B @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(826,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(53,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(711,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(1428,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(253,axiom,
( c_Arrow__Order__Mirabelle_OProf
= ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_FuncSet_OPi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Prof__def) ).
thf(1503,plain,
( c_Arrow__Order__Mirabelle_OProf
= ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_FuncSet_OPi ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2293,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1271,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( D @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
thf(611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( D @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(54,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(713,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(1332,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(1090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
thf(1224,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(385,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(2055,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(1092,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(2557,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(1464,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(947,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(2148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1356,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(2079,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= A )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).
thf(2119,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= A )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(2624,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
thf(2493,plain,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(784,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(1048,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(1722,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( D @ ( E @ ( F @ c_List_Olist_Olist__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
thf(1043,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( D @ ( E @ ( F @ c_List_Olist_Olist__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(1690,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(1571,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert ) ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
thf(1307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert ) ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(389,axiom,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ofinite ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
thf(2065,plain,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ofinite ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(1853,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(996,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
thf(616,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(1122,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
thf(2180,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(2632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
thf(535,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(769,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(1029,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(95,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(895,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
thf(1293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( F @ ( B @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( F @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).
thf(932,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( ( F @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
thf(1952,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(2578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj) ).
thf(1688,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(685,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( E @ ( D @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
thf(983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( E @ ( D @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(1926,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1594,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(1245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(1445,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(410,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
thf(2139,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(120,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(986,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(1775,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(2022,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(509,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
thf(2535,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(314,axiom,
v_Lba____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(1726,plain,
v_Lba____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(2303,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(417,axiom,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( v_n____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I1_J) ).
thf(2156,plain,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( v_n____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(2207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(501,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
thf(2506,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( A @ c_Int_Oring__1__class_OInts @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
thf(959,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2171,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(373,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(2005,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1626,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
thf(722,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(1467,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(431,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(2202,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(518,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(2564,plain,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(81,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(823,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(1551,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(182,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1203,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(1208,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(459,axiom,
~ ( v_Lba____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(2318,plain,
~ ( v_Lba____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(2271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(43,axiom,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(680,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(1277,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
thf(2234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(162,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(1134,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( B @ ( D @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
thf(648,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( B @ ( D @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(2513,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(855,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(1025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(1611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(50,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(707,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(412,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2143,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
thf(1647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(2175,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( D @ c_Finite__Set_Ocard ) @ ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(2386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( D @ c_Finite__Set_Ocard ) @ ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(1230,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(10,axiom,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
thf(557,plain,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(125,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
thf(1003,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(256,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(1516,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(1598,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(31,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
thf(640,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(1961,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(1605,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(523,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] : ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_third__alt) ).
thf(2588,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] : ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
thf(1941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(954,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(1987,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(791,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(2276,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(808,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(2044,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(160,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(1130,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(1218,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(1220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(1053,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(251,axiom,
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjh) ).
thf(1499,plain,
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(1432,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(2165,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( C @ c_List_Osplice ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
thf(576,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( C @ c_List_Osplice ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(1658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(907,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(1934,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(1543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(2113,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(165,axiom,
~ ! [A: $i] :
( ( A @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1141,plain,
~ ! [A: $i] :
( ( A @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(1702,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(460,axiom,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(2320,plain,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(727,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(1094,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(1008,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
thf(595,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(2266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(1617,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ ( C @ c_COMBK ) @ ( D @ ( C @ ( A @ tc_fun ) @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( C @ ( A @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
thf(2500,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ ( C @ c_COMBK ) @ ( D @ ( C @ ( A @ tc_fun ) @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( C @ ( A @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(744,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist_Olist__case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
thf(600,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist_Olist__case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(413,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2145,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( A @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
thf(1421,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( A @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(2458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(2088,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(1553,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(2226,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(1866,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(1321,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(1834,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(1844,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(688,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(186,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1216,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(2209,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(402,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(2110,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(1010,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(456,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2305,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(1575,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(2591,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(296,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1646,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(1326,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).
thf(1253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__less) ).
thf(963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
thf(748,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1639,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(2251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(1481,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1629,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__image) ).
thf(2026,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(525,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2608,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(1822,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(259,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(1523,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(786,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(2416,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(2135,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(475,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(2406,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
thf(1558,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(415,axiom,
~ ( v_Lab____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(2152,plain,
~ ( v_Lab____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(2384,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1777,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(667,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1440,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(2198,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
thf(2066,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(1193,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
thf(2162,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(300,axiom,
! [A: $i] :
( ( A @ c_Arrow__Order__Mirabelle_OIIA )
<=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1661,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) )
=> ( A @ c_Arrow__Order__Mirabelle_OIIA ) )
& ( ( A @ c_Arrow__Order__Mirabelle_OIIA )
=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(2095,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
thf(549,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= B )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
thf(1607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= B )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(763,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(716,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(1161,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) )
& ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(800,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(2123,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
<=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(2517,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(967,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
thf(818,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(603,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(1578,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(364,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(1957,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(950,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1097,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(371,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(1989,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(1816,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1693,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ ( B @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C3_C) ).
thf(1172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( E @ ( B @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
thf(664,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(397,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(2091,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(2619,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(2549,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(500,axiom,
~ ! [A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_d____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(2502,plain,
~ ! [A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_d____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1827,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).
thf(1268,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_Olist__size ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2485,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) )
<=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(2467,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) )
& ( ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(992,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(1923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(235,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(1431,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(691,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(492,axiom,
v_n____ @ ( v_h____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( v_P____ @ hAPP ) @ ( v_d____ @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096) ).
thf(2484,plain,
v_n____ @ ( v_h____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( v_P____ @ hAPP ) @ ( v_d____ @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(2372,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( C
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(624,plain,
! [A: $i,B: $i,C: $i] :
( C
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(85,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(839,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(419,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Nat_Onat_Onat__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
thf(2159,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Nat_Onat_Onat__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(1352,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(1977,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1532,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(860,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(1505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(1621,plain,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(1737,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(481,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( B @ c_FuncSet_OPi ) ) ) @ ( B @ c_COMBI @ ( B @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
thf(2436,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( B @ c_FuncSet_OPi ) ) ) @ ( B @ c_COMBI @ ( B @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2453,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(2191,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(708,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(461,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(2321,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
thf(1367,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( E @ ( C @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(2438,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( F @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij) ).
thf(1490,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( F @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(134,axiom,
! [A: $i] :
( ( v_n____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I2_J) ).
thf(1037,plain,
! [A: $i] :
( ( v_n____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(69,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(775,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
thf(1917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(676,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) )
=> ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(2848,plain,
$false,
inference(e,[status(thm)],[892,2630,1501,2612,1168,1454,1729,1237,2544,555,1549,1686,2072,1767,628,1031,2077,1158,1005,2117,683,2062,1443,741,2282,655,614,1041,1750,977,1305,597,1078,1310,2448,913,2580,1954,538,1497,2195,1705,797,2316,1275,2141,1222,2360,1196,1243,2020,1613,2010,1921,1601,1724,2531,1228,2432,1914,973,1046,2400,1529,1518,1265,2039,719,2269,1330,2274,1313,1832,1992,1132,1055,724,1760,1660,587,1323,1545,559,2403,1247,969,1013,1568,2024,1963,2388,1847,2456,2237,924,2616,2324,2105,591,1911,623,834,1151,2291,1581,1283,1109,1632,2508,2058,2618,634,2424,660,2242,2103,1447,956,2523,2530,1526,2137,2392,2154,1863,1074,1206,920,2204,1153,810,2047,534,1636,1057,1438,661,546,793,1199,2164,1470,1708,1067,2496,2621,714,2382,2441,1900,2560,2249,1255,2133,820,630,1824,729,1560,952,2541,1938,1365,2477,1296,1819,1836,1195,710,852,1555,2313,551,2492,1634,2228,1910,842,2300,2157,1851,650,1328,1064,980,2509,1540,857,1360,1936,2498,1234,1856,725,1138,2537,1493,642,2240,1791,1214,590,1155,1419,637,1584,1039,970,837,2285,1297,738,1974,2243,1932,911,2006,2566,1002,1874,1715,1720,1759,2450,1588,1099,1150,1249,2465,1050,2546,2043,1695,657,1187,2408,2189,926,1814,1086,1712,1846,2076,1170,1286,2368,1466,1071,1135,1146,2391,1273,1747,2028,573,965,1727,1251,2413,1959,1103,694,1916,1615,2489,1752,1929,2568,579,1403,2398,1520,1124,826,711,1428,1503,2293,1271,611,713,1332,1090,1224,2055,1092,1897,2557,1464,947,2148,1356,2079,2119,2624,2493,784,1524,1048,1722,1043,1690,1571,1307,2065,1853,1408,990,996,616,1122,2180,2632,1339,535,848,769,1029,895,1293,2553,932,1952,2578,1688,685,983,1926,1594,1245,1445,2139,1015,986,1775,2022,2535,1726,2303,2156,2207,653,2069,2506,959,2171,2005,1626,722,2107,1467,2202,2564,823,1551,1203,1208,2318,2271,680,1277,2234,1134,648,2513,776,855,1025,872,1611,707,2143,1647,2175,2386,1230,557,1003,1516,1598,640,1961,1605,2588,1941,954,1987,791,2276,808,2044,1130,1218,1220,1053,1499,1432,2165,576,1658,544,907,1934,1543,2113,1141,1702,2320,727,1094,1008,595,2266,1617,2056,2247,2500,744,600,2145,1421,2458,2088,1553,1412,2226,1866,1321,1834,1844,688,903,1216,2209,2110,1010,2305,1575,2591,1646,1326,1253,963,748,1639,2251,1481,1629,2026,2608,1822,1523,786,2416,2135,2406,1558,2152,2384,1777,667,1440,2198,2066,1193,2162,1661,2095,549,1607,763,716,1161,800,2123,1512,2517,967,818,1148,603,1578,1957,950,1097,1989,1816,1693,1172,664,2091,2619,696,2549,928,2502,1827,1268,2485,2467,992,1923,1431,691,2484,1120,2372,624,839,2159,1352,1829,1977,1532,860,1505,1621,1737,2436,2453,2191,708,2321,1367,2438,1490,1037,775,1917,676,882,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT162+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/10.50 % Computer : n014.cluster.edu
% 0.24/10.50 % Model : x86_64 x86_64
% 0.24/10.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/10.50 % Memory : 8046.5625MB
% 0.24/10.50 % OS : Linux 6.8.0-71-generic
% 0.24/10.50 % CPULimit : 300
% 0.24/10.50 % WCLimit : 300
% 0.24/10.50 % DateTime : Sat Sep 26 06:34:43 UTC 2026
% 0.24/10.50 % CPUTime :
% 0.24/10.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.26/10.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.66/11.06 % [INFO] Parsing done (258ms).
% 1.66/11.07 % [INFO] Running in sequential loop mode.
% 2.42/11.27 % [INFO] eprover registered as external prover.
% 2.42/11.28 % [INFO] Scanning for conjecture ...
% 3.20/11.44 % [INFO] Found a conjecture (or negated_conjecture) and 531 axioms. Running axiom selection ...
% 4.18/11.61 % [INFO] Axiom selection finished. Selected 531 axioms (removed 0 axioms).
% 5.17/11.87 % [INFO] Problem is first-order (TPTP FOF).
% 5.63/11.90 % [INFO] Type checking passed.
% 5.63/11.90 % [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 ...
% 23.85/15.61 % External prover 'e' found a proof!
% 23.85/15.61 % [INFO] Killing All external provers ...
% 23.85/15.61 % Time passed: 5015ms (effective reasoning time: 4535ms)
% 23.85/15.61 % 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)>
% 23.85/15.61 % Axioms used in derivation (531): fact_add__le__less__mono, fact_xt1_I1_J, fact_le__SucI, fact_Pi__I, fact_insertCI, fact_surj__f__inv__f, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_card__image__le, arity_fun__Orderings_Oorder, fact_folding__image__simple__idem_Osubset__idem, fact_nat_Osimps_I3_J, fact_pos__add__strict, fact_n_I2_J, fact_add__strict__right__mono, fact_Ints__odd__nonzero, fact_inj__imp__surj__inv, fact_subset__UNIV, fact_inv__into__into, fact_insert__iff, fact_le__eq__less__or__eq, fact_xt1_I4_J, fact_unanimity__def, fact_trans__less__add1, fact_injD, fact_folding__image__simple__idem_Oin__idem, fact_nat__add__left__commute, fact_order__le__less__trans, fact_image__insert, fact__C1_C, fact_nat__less__cases, fact_Pi__mono, arity_prod__Finite__Set_Ofinite, fact_IIA__def, fact_one__is__add, fact_surjh, fact_funcset__image, fact_termination__basic__simps_I5_J, fact_insert__subset, arity_Nat__Onat__Orderings_Oorder, fact__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_Suc__mono, fact_insertI1, fact_order__less__asym_H, fact_third__alt, fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_less__imp__le__nat, fact_add__leD1, arity_sum__Finite__Set_Ofinite, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, fact_nat_Osize_I4_J, fact_linorder__not__le, fact_finite, fact_add__less__mono, fact_order__eq__refl, arity_Nat__Onat__Rings_Ozero__neq__one, fact_in__mktop, fact_add__right__imp__eq, fact_finite__range__imageI, fact_linorder__neqE, fact_leI, fact_assms_I1_J, fact_Suc__le__mono, fact_inj__image__mem__iff, fact_Pi__anti__mono, fact_linorder__antisym__conv2, fact_measures__lesseq, arity_HOL__Obool__Orderings_Opreorder, fact_nat__add__right__cancel, fact_PiProf, fact_gr0__conv__Suc, fact_in__mkbot, fact_surj__iff__all, help_c__fequal__2, fact_le__neq__implies__less, fact_add__pos__nonneg, fact_finite__code, fact_zero__le__one, fact_linorder__neqE__linordered__idom, help_c__COMBC__1, fact_finite__Plus__UNIV__iff, fact_below__Lin, fact_nat__add__left__cancel__less, fact_pred__equals__eq2, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_linorder__antisym__conv3, fact_add__strict__increasing2, fact_order__less__imp__not__eq, fact_image__image, fact__C4_C, fact_add__le__imp__le__left, arity_Option__Ooption__Finite__Set_Ofinite, fact_list_Osimps_I3_J, fact_linorder__antisym__conv1, fact_add__nonneg__eq__0__iff, fact_inv__into__image__cancel, fact_measures__less, fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_card__eq__UNIV__imp__eq__UNIV, fact_add__increasing2, fact_splice_Osimps_I3_J, fact_equalityD2, fact_even__less__0__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_add__0__left, fact_add__mono, fact_add__0__iff, fact_le__funD, fact_add__right__mono, fact_le__fun__def, fact_finite__Prod__UNIV, fact_finite__UNIV, fact_Pi__mem, fact_predicate2D, fact_gr0I, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact__096c_A_126_061_Ad_096, fact_inj__on__inv__into, fact_splice_Osimps_I2_J, fact_list_Osize_I2_J, arity_HOL__Obool__Orderings_Otop, fact_order__less__imp__not__less, fact_folding__image__simple__idem_Oinsert__idem, fact_less__eq__nat_Osimps_I1_J, fact_lessI, fact_ord__less__eq__trans, fact_in__mono, fact_zero__reorient, fact_termination__basic__simps_I4_J, fact_le__iff__add, fact_one__reorient, fact_top__apply, help_c__COMBS__1, fact_xt1_I9_J, fact_less__add__eq__less, help_c__COMBI__1, fact_linorder__less__linear, fact_add__lessD1, fact_add__le__mono1, fact_card__image, fact_mkbot__Lin, fact_list_Osimps_I2_J, fact_in__measure, fact_Suc__less__SucD, fact_add__0__right, fact_card__bij, fact_subset__iff__psubset__eq, fact_nat_Oinject, fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_not__add__less2, fact_less__or__eq__imp__le, fact_funcset__mem, fact_top1I, fact_rev__image__eqI, fact_Suc__leI, fact_add__neg__nonpos, fact_in__finite__psubset, fact_inj__on__contraD, fact_not__less__less__Suc__eq, fact_finite__imageD, fact_card__Plus__conv__if, fact_UNIV__I, fact_le__add2, fact_inj__on__strict__subset, arity_Nat__Onat__Orderings_Opreorder, fact_finite__indi, fact_card__bij__eq, fact_finite__surj, fact_Suc__n__not__le__n, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_Suc__lessD, fact_order__less__imp__not__eq2, fact_order__refl, fact_not__less0, fact_card__psubset, fact_dictator__def, fact_add__left__imp__eq, fact_trans__less__add2, fact_less__Suc__eq__le, fact_card_Oinsert, fact_add__leD2, fact_xt1_I5_J, fact_insert__code, fact_Ints__0, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_inj__on__id2, fact_not__one__less__zero, fact_not__less__eq, fact_zero__le__double__add__iff__zero__le__single__add, fact_nat__neq__iff, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_insert__image, fact_nat_Osimps_I2_J, fact_finite__PlusD_I2_J, fact__C2_C, fact_add__right__cancel, fact_add__less__cancel__left, fact_add__left__cancel, fact_eq__mem, fact_distinct_Osimps_I1_J, fact_finite__UNIV__card__ge__0, fact_nat__size, fact_subset__insertI, fact_notin__Lin__iff, fact_xt1_I3_J, fact_less__imp__neq, fact_xt1_I8_J, fact_predicate1D, fact_less__not__refl3, fact_inj__eq, fact_nat__add__left__cancel__le, fact_double__zero__sym, arity_HOL__Obool__Orderings_Oord, fact__096a_A_126_061_Ab_096, fact_finite__insert, fact_one__neq__zero, fact_insert__absorb2, fact_list_Oinject, fact_insertI2, fact_less__Suc__eq__0__disj, fact_le__Suc__eq, fact_insert__absorb, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_finite__fun__UNIVD1, fact_add__strict__mono, fact_inj__image__eq__iff, fact_subset__insert, fact__096Lba_A_058_ALin_096, fact_rev__finite__subset, arity_Nat__Onat__Groups_Ocomm__monoid__add, fact_eqset__imp__iff, fact_same__fstI, fact_less__antisym, fact_order__neq__le__trans, fact_not__one__le__zero, fact_Suc__le__eq, fact_range__composition, fact_equalityD1, fact_finite__option__UNIV, fact_subset__image__iff, fact_le__funE, fact_inj__on__def, fact_inj__on__iff, arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Groups_Omonoid__add, arity_fun__Orderings_Opreorder, fact_less__eq__Suc__le, fact_less__add__Suc2, fact_insert__commute, fact_in__below, help_c__fequal__1, fact_in__above, fact_finite__imageI, fact_ord__le__eq__trans, fact_linorder__neq__iff, fact_inv__image__comp, fact_folding__image__simple_Oinsert, fact_nat_Osize_I1_J, fact_range__ex1__eq, fact_not__Cons__self, fact_mlex__leq, fact_psubset__card__mono, fact_not__less__iff__gr__or__eq, fact_card__ge__0__finite, fact_inj__image__subset__iff, arity_Nat__Onat__Groups_Ozero, fact_add__is__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_set__mp, fact_injh, fact_linorder__neqE__nat, fact_mktop__Lin, fact__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_psubsetD, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, fact_card__insert__if, fact_order__less__le, fact__096Lab_A_058_ALin_096, fact_card__Plus, fact_add__nonneg__pos, fact_add__less__cancel__right, fact_add__nonpos__nonpos, fact_set__eq__subset, fact_inv__into__injective, fact_psubset__trans, fact_xt1_I12_J, fact_Ints__double__eq__0__iff, fact_subset__inj__on, fact_Suc__le__lessD, fact_add__increasing, fact_not__add__less1, fact_pred__subset__eq, arity_Product____Type__Ounit__Finite__Set_Ofinite, fact_n_I3_J, fact_Suc__inject, fact_subset__refl, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_fun__Finite__Set_Ofinite, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_zero__less__double__add__iff__zero__less__single__add, fact_Suc__neq__Zero, fact_card__mono, fact_add__eq__self__zero, arity_fun__Orderings_Oord, fact_equalityI, fact_ext, fact_order__less__not__sym, arity_HOL__Obool__Orderings_Oorder, fact_linorder__le__less__linear, fact_nat__add__left__cancel, fact_endo__inj__surj, fact_Prof__def, arity_Nat__Onat__Orderings_Olinorder, fact_PiE, fact_assms_I3_J, fact_Pi__UNIV, fact_in__measures_I2_J, fact_Ints__1, fact_less__le__not__le, fact_n__not__Suc__n, fact_nat__le__linear, fact_inv__into__f__f, fact_linorder__le__cases, fact_card__UNIV__unit, fact_order__less__le__trans, help_c__COMBB__1, fact_card__inj__on__le, fact_rangeI, fact_not__leE, fact_insert__ident, fact_add__Suc, fact_order__less__asym, fact_add__gr__0, arity_fun__Orderings_Otop, fact_nat_Osize_I2_J, fact_leD, fact_add__strict__left__mono, fact_mlex__less, fact_psubset__imp__subset, fact_funcset__id, fact_set__rev__mp, fact_card__insert__disjoint, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, fact_eq__mem__trans, fact_inj__on__iff__eq__card, fact_Suc__eq__plus1__left, fact_Zero__not__Suc, fact_inv__f__f, fact_not__Cons__self2, fact_Suc__leD, fact_zero__less__one, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_add_Ocomm__neutral, fact_add__less__imp__less__right, fact_ex__nat__less__eq, fact_list_Osimps_I5_J, fact_pigeonhole, fact_image__surj__f__inv__f, fact_rev__predicate2D, fact_linorder__linear, fact_less__eq__Suc__le__raw, fact_less__trans__Suc, fact_xt1_I6_J, fact_subset__insertI2, arity_HOL__Obool__Finite__Set_Ofinite, fact_less__not__refl2, fact_inj__fun, fact_le__add1, fact_trans__le__add2, fact_le__refl, fact_nat__add__assoc, fact_linorder__not__less, fact_add__neg__neg, fact_add__less__imp__less__left, fact__096P_A_058_AProf_096, fact_le__imp__less__Suc, fact_in__measures_I1_J, fact_xt1_I2_J, fact_less__add__Suc1, fact_all__nat__less__eq, fact_less__fun__def, fact_rev__predicate1D, fact_One__nat__def, fact_in__lex__prod, fact_add__is__0, fact_Ints__odd__less__0, fact_termination__basic__simps_I3_J, fact_image__inv__into__cancel, fact_inv__f__eq, fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_add__pos__pos, fact_add__0, fact_equalityE, fact_add__nonneg__nonneg, fact_Suc__eq__plus1, fact_in__rel__def, fact_subset__psubset__trans, fact_card__inj, fact_Zero__neq__Suc, fact_order__eq__iff, fact_image__iff, fact_Lin__irrefl, fact_card__seteq, fact_finite__fun__UNIVD2, arity_Nat__Onat__Groups_Oab__semigroup__add, fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096, fact_not__less__eq__eq, fact_insert__mono, fact_ord__eq__less__trans, fact_le0, fact_ex__least__nat__less, fact_le__trans, fact_equalityCE, fact_gr__implies__not0, fact_finite_OinsertI, help_c__COMBK__1, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, fact_add__left__mono, fact_pairwise__neutrality, fact_double__add__le__zero__iff__single__add__le__zero, fact_less__not__refl, fact_less__add__one, fact_inj__on__add__nat, fact_zero__neq__one, fact_less__Suc__eq, fact_nat__add__commute, fact_above__Lin, fact_range__eqI, fact_u, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_add__less__le__mono, fact_dist, fact_Ints__add, fact_image__eqI, fact_subsetD, fact_top__greatest, fact_Suc__less__eq, fact_splice__Nil2, fact_eq__card__imp__inj__on, fact_psubset__eq, fact_add__leE, fact_image__ident, fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096, fact_zero__less__Suc, fact_dictatorI, fact_inv__into__f__eq, fact_image__mono, fact_plus__nat_Oadd__0, fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_order__le__imp__less__or__eq, fact_inj__Suc, fact_add__nonpos__neg, fact_list_Osimps_I4_J, fact_finite__PlusD_I1_J, fact_le__SucE, fact_eq__imp__le, fact_finite__surj__inj, fact_nat_Osize_I3_J, fact_add__strict__increasing, fact_insertE, fact_le__less__Suc__eq, fact_inj__onD, fact_splice_Osimps_I1_J, fact_Suc__n__not__n, fact_f__inv__into__f, fact_subset__trans, fact_le__antisym, fact_trans__le__add1, fact_eqelem__imp__iff, fact_card__infinite, fact_pred__equals__eq, fact_finite__UNIV__surj__inj, fact_psubset__subset__trans, fact_order__antisym__conv, fact_n_I1_J, fact_neq0__conv, fact_double__eq__0__iff, fact_le__0__eq, fact_finite__UNIV__inj__surj, fact_zero__less__two, fact__C3_C, fact_add__le__imp__le__right, fact_order__less__irrefl, fact_add__le__mono, fact_less__Suc0, fact_order__le__less, fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_iso__tuple__UNIV__I, fact_less__iff__Suc__add, fact_order__less__imp__le, fact_termination__basic__simps_I1_J, fact_finite__subset, fact_order__less__trans, fact_add__imp__eq, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_nat__less__le, fact_list_Osize_I1_J, fact_less__SucE, fact_ord__eq__le__trans, fact_finite__Plus, fact_double__add__less__zero__iff__single__add__less__zero, fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Nat__Onat__Groups_Oone, fact_mem__def, fact_pred__subset__eq2, fact_card__insert__le, fact_linorder__cases, fact_xt1_I11_J, fact_add__less__mono1, fact_add__le__cancel__left, fact_add__Suc__shift, fact_xt1_I7_J, fact_order__trans, fact_image__inv__f__f, fact_finite__Plus__iff, fact_imageI, fact_less__SucI, fact_Suc__not__Zero, fact_folding__image__simple__idem_Oidem, fact_surj__imp__inj__inv, fact_Suc__lessI, fact_add__Suc__right, fact_const__Lin__Prof, fact_UNIV__Plus__UNIV
% 23.85/15.61 % No. of inferences in proof: 1066
% 23.85/15.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5015 ms resp. 4535 ms w/o parsing
% 24.76/15.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.76/15.89 % [INFO] Killing All external provers ...
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