%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT163+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 : n020.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 33.12s 8.41s
% Output : Refutation 37.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 533
% Syntax : Number of formulae : 1068 ( 265 unt; 0 typ; 0 def)
% Number of atoms : 3075 ( 776 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 24548 ( 348 ~; 72 |; 266 &;22193 @)
% ( 125 <=>;1544 =>; 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 : 104 ( 102 usr; 25 con; 0-6 aty)
% Number of variables : 3080 ( 0 ^;3047 !; 33 ?;3080 :)
% 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_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(v_c_____decl,type,
v_c____: $i ).
thf(v_d_____decl,type,
v_d____: $i ).
thf(v_P_____decl,type,
v_P____: $i ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $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_e_____decl,type,
v_e____: $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Hilbert__Choice_Oinv__into_decl,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $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_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
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_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $i > $o ).
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(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_decl,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_b_____decl,type,
v_b____: $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(c_fequal_decl,type,
c_fequal: $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_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
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(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_If_decl,type,
c_If: $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(c_Arrow__Order__Mirabelle_OProf_decl,type,
c_Arrow__Order__Mirabelle_OProf: $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_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(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_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__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Wellfounded_Omlex__prod_decl,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__image_decl,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $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(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(c_fFalse_decl,type,
c_fFalse: $i ).
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(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_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $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_Nitpick_Orefl_H_decl,type,
c_Nitpick_Orefl_H: $i > $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(426,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(2199,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)],[426]) ).
thf(275,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(1586,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)],[275]) ).
thf(219,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(1337,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(229,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(1369,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)],[229]) ).
thf(460,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(2341,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)],[460]) ).
thf(321,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(1767,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)],[321]) ).
thf(372,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(1995,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)],[372]) ).
thf(93,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(846,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)],[93]) ).
thf(352,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(1899,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)],[352]) ).
thf(520,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(2595,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)],[520]) ).
thf(118,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(962,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)],[118]) ).
thf(508,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(2559,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)],[508]) ).
thf(112,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(941,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)],[112]) ).
thf(458,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(2331,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)],[458]) ).
thf(3,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(555,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(263,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(1554,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)],[263]) ).
thf(412,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(2163,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)],[412]) ).
thf(101,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(892,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)],[101]) ).
thf(26,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(628,plain,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(130,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(1031,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)],[130]) ).
thf(35,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(666,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)],[35]) ).
thf(204,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(1295,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)],[204]) ).
thf(317,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(1750,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)],[317]) ).
thf(140,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(1068,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(533,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(2659,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)],[533]) ).
thf(499,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(2527,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)],[499]) ).
thf(268,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 ) ) ) ) ) )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( D @ ( C @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(1569,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 ) ) ) ) ) )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( D @ ( C @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(163,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(1142,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)],[163]) ).
thf(248,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(1486,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)],[248]) ).
thf(168,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(1158,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)],[168]) ).
thf(494,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(2512,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)],[494]) ).
thf(307,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(1692,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)],[307]) ).
thf(37,axiom,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(677,plain,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(251,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(1497,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)],[251]) ).
thf(300,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(1671,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)],[300]) ).
thf(281,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(1608,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)],[281]) ).
thf(161,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(1137,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)],[161]) ).
thf(522,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(2607,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)],[522]) ).
thf(382,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(2035,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)],[382]) ).
thf(340,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(1867,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)],[340]) ).
thf(188,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1233,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(218,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(1327,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)],[218]) ).
thf(291,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(1640,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)],[291]) ).
thf(359,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(1954,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)],[359]) ).
thf(110,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(930,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(514,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(2575,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)],[514]) ).
thf(486,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(2476,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)],[486]) ).
thf(43,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(698,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(103,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(898,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)],[103]) ).
thf(335,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(1835,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)],[335]) ).
thf(379,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(2020,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)],[379]) ).
thf(293,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(1650,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(234,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(1386,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)],[234]) ).
thf(388,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(2067,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)],[388]) ).
thf(501,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(2531,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)],[501]) ).
thf(347,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(1887,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)],[347]) ).
thf(490,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(2491,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)],[490]) ).
thf(327,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(1782,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)],[327]) ).
thf(99,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(885,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)],[99]) ).
thf(131,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(1046,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)],[131]) ).
thf(7,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(565,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)],[7]) ).
thf(228,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(1366,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)],[228]) ).
thf(405,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(2136,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)],[405]) ).
thf(310,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(1703,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)],[310]) ).
thf(287,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(1628,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)],[287]) ).
thf(202,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(1287,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)],[202]) ).
thf(457,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(2328,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)],[457]) ).
thf(329,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(1792,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)],[329]) ).
thf(319,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(1760,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)],[319]) ).
thf(78,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(802,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)],[78]) ).
thf(421,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(2185,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)],[421]) ).
thf(489,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(2488,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)],[489]) ).
thf(115,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(949,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)],[115]) ).
thf(135,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(1055,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)],[135]) ).
thf(54,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(724,plain,
! [A: $i,B: $i,C: $i] :
( C
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(479,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(2444,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)],[479]) ).
thf(337,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(1860,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)],[337]) ).
thf(430,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(2217,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)],[430]) ).
thf(13,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(587,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)],[13]) ).
thf(216,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(1323,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)],[216]) ).
thf(255,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(1511,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)],[255]) ).
thf(107,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(917,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)],[107]) ).
thf(45,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(702,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)],[45]) ).
thf(470,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(2420,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)],[470]) ).
thf(5,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(559,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)],[5]) ).
thf(415,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(2169,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)],[415]) ).
thf(247,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(1479,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)],[247]) ).
thf(313,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(1741,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)],[313]) ).
thf(496,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(2520,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)],[496]) ).
thf(344,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(1875,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)],[344]) ).
thf(384,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(2049,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)],[384]) ).
thf(507,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(2552,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)],[507]) ).
thf(214,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(1319,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)],[214]) ).
thf(349,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(1890,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)],[349]) ).
thf(19,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(606,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)],[19]) ).
thf(223,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(1347,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)],[223]) ).
thf(269,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(1572,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)],[269]) ).
thf(419,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(2178,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)],[419]) ).
thf(311,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(1714,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)],[311]) ).
thf(15,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(591,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)],[15]) ).
thf(531,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(2650,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(303,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(1682,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)],[303]) ).
thf(302,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(1677,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)],[302]) ).
thf(362,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(1960,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)],[362]) ).
thf(174,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(1183,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)],[174]) ).
thf(378,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(2017,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)],[378]) ).
thf(249,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(1489,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)],[249]) ).
thf(437,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(2237,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)],[437]) ).
thf(397,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(2105,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)],[397]) ).
thf(332,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(1811,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)],[332]) ).
thf(154,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(1109,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)],[154]) ).
thf(288,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(1632,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)],[288]) ).
thf(240,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(1418,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)],[240]) ).
thf(481,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(2451,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)],[481]) ).
thf(24,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(623,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(336,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(1858,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)],[336]) ).
thf(401,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(2122,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)],[401]) ).
thf(9,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(574,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)],[9]) ).
thf(438,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(2254,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)],[438]) ).
thf(133,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(1051,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)],[133]) ).
thf(84,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(821,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(41,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(687,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)],[41]) ).
thf(142,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(1072,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)],[142]) ).
thf(33,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(660,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)],[33]) ).
thf(375,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(2002,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)],[375]) ).
thf(222,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(1345,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)],[222]) ).
thf(357,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(1943,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)],[357]) ).
thf(278,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(1600,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)],[278]) ).
thf(256,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(1521,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)],[256]) ).
thf(428,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(2205,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)],[428]) ).
thf(517,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(2586,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)],[517]) ).
thf(367,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(1975,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)],[367]) ).
thf(18,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(602,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,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(766,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)],[68]) ).
thf(351,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(1896,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)],[351]) ).
thf(98,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(877,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)],[98]) ).
thf(423,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(2190,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)],[423]) ).
thf(155,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(1119,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)],[155]) ).
thf(472,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(2424,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)],[472]) ).
thf(152,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(1104,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)],[152]) ).
thf(94,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(849,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)],[94]) ).
thf(338,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(1863,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)],[338]) ).
thf(178,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(1206,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)],[178]) ).
thf(38,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(678,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)],[38]) ).
thf(75,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(793,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)],[75]) ).
thf(108,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(925,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)],[108]) ).
thf(464,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(2364,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)],[464]) ).
thf(66,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(761,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(245,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(1470,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)],[245]) ).
thf(435,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(2232,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)],[435]) ).
thf(527,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(2641,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)],[527]) ).
thf(374,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(2000,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)],[374]) ).
thf(50,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(714,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)],[50]) ).
thf(341,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(1868,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)],[341]) ).
thf(518,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(2589,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(102,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(894,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)],[102]) ).
thf(60,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(746,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)],[60]) ).
thf(156,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(1123,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)],[156]) ).
thf(408,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(2147,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)],[408]) ).
thf(253,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(1502,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)],[253]) ).
thf(27,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(630,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(73,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(788,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)],[73]) ).
thf(403,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(2132,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(191,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(1238,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)],[191]) ).
thf(266,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(1560,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)],[266]) ).
thf(197,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(1274,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)],[197]) ).
thf(478,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(2441,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)],[478]) ).
thf(221,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(1343,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)],[221]) ).
thf(509,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(2560,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)],[509]) ).
thf(446,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(2277,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)],[446]) ).
thf(225,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(1355,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)],[225]) ).
thf(272,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(1580,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)],[272]) ).
thf(171,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(1174,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)],[171]) ).
thf(404,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(2133,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)],[404]) ).
thf(381,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(2032,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)],[381]) ).
thf(80,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(815,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(241,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(1423,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)],[241]) ).
thf(279,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(1602,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(227,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(1365,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(25,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(625,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)],[25]) ).
thf(95,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(852,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)],[95]) ).
thf(172,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(1178,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)],[172]) ).
thf(333,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(1819,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)],[333]) ).
thf(420,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 ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
thf(2179,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ 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__eq ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(144,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(1079,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)],[144]) ).
thf(39,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(682,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(454,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(2313,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)],[454]) ).
thf(11,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(583,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)],[11]) ).
thf(523,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(2609,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)],[523]) ).
thf(88,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(830,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)],[88]) ).
thf(532,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(2653,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)],[532]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(1106,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(189,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(1234,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)],[189]) ).
thf(358,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(1953,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(331,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(1804,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)],[331]) ).
thf(462,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(2359,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)],[462]) ).
thf(138,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(1064,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)],[138]) ).
thf(242,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(1425,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)],[242]) ).
thf(503,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(2537,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(442,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(2268,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)],[442]) ).
thf(122,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(989,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)],[122]) ).
thf(237,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(1397,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)],[237]) ).
thf(145,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(1082,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(363,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(1964,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)],[363]) ).
thf(111,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(933,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)],[111]) ).
thf(243,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(1461,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)],[243]) ).
thf(390,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(2080,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)],[390]) ).
thf(180,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(1214,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)],[180]) ).
thf(398,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(2108,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)],[398]) ).
thf(392,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(2085,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)],[392]) ).
thf(283,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(1612,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)],[283]) ).
thf(167,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(1155,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)],[167]) ).
thf(239,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(1414,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)],[239]) ).
thf(385,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(2053,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)],[385]) ).
thf(348,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(1889,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)],[348]) ).
thf(292,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(1644,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)],[292]) ).
thf(92,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(837,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)],[92]) ).
thf(150,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(1099,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)],[150]) ).
thf(495,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(2519,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)],[495]) ).
thf(205,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(1297,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)],[205]) ).
thf(452,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(2304,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)],[452]) ).
thf(232,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(1382,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)],[232]) ).
thf(187,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(1231,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)],[187]) ).
thf(158,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(1131,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)],[158]) ).
thf(511,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(2566,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)],[511]) ).
thf(371,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(1984,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)],[371]) ).
thf(124,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(1002,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)],[124]) ).
thf(369,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(1979,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)],[369]) ).
thf(377,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(2006,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)],[377]) ).
thf(51,axiom,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(721,plain,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(427,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(2203,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)],[427]) ).
thf(146,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(1086,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)],[146]) ).
thf(325,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(1779,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)],[325]) ).
thf(429,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(2208,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)],[429]) ).
thf(308,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(1695,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)],[308]) ).
thf(244,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(1466,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)],[244]) ).
thf(528,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(2645,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)],[528]) ).
thf(524,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(2617,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)],[524]) ).
thf(500,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(2529,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)],[500]) ).
thf(192,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(1241,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)],[192]) ).
thf(506,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(2546,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)],[506]) ).
thf(175,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(1187,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)],[175]) ).
thf(36,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(674,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)],[36]) ).
thf(468,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(2408,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)],[468]) ).
thf(297,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(1663,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)],[297]) ).
thf(436,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(2235,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)],[436]) ).
thf(353,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(1906,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)],[353]) ).
thf(160,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(1135,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(194,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(1251,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)],[194]) ).
thf(418,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(2176,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)],[418]) ).
thf(165,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(1146,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)],[165]) ).
thf(361,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(1959,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(86,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(824,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)],[86]) ).
thf(512,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(2570,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)],[512]) ).
thf(96,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(856,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)],[96]) ).
thf(207,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(1301,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)],[207]) ).
thf(497,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(2524,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(445,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(2275,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)],[445]) ).
thf(409,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(2149,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)],[409]) ).
thf(83,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(819,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)],[83]) ).
thf(383,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(2048,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(157,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(1125,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)],[157]) ).
thf(498,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(2525,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)],[498]) ).
thf(70,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(772,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(235,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(1388,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)],[235]) ).
thf(59,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(743,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)],[59]) ).
thf(10,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(577,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)],[10]) ).
thf(6,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(562,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)],[6]) ).
thf(104,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(904,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)],[104]) ).
thf(284,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(1615,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)],[284]) ).
thf(328,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(1784,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)],[328]) ).
thf(411,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(2161,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)],[411]) ).
thf(211,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(1312,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)],[211]) ).
thf(289,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(1635,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)],[289]) ).
thf(136,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(1058,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)],[136]) ).
thf(373,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(1997,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)],[373]) ).
thf(148,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(1092,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)],[148]) ).
thf(79,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(804,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)],[79]) ).
thf(485,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(2474,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)],[485]) ).
thf(425,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(2193,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)],[425]) ).
thf(299,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(1669,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)],[299]) ).
thf(290,axiom,
~ ( c_fFalse @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1638,plain,
~ ( c_fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(185,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(1224,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)],[185]) ).
thf(513,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(2573,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)],[513]) ).
thf(455,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(2319,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)],[455]) ).
thf(121,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(979,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)],[121]) ).
thf(504,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(2538,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)],[504]) ).
thf(391,axiom,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(2084,plain,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(270,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(1574,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)],[270]) ).
thf(258,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(1524,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)],[258]) ).
thf(224,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(1349,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)],[224]) ).
thf(276,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(1589,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)],[276]) ).
thf(450,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(2299,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)],[450]) ).
thf(164,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(1144,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)],[164]) ).
thf(57,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(737,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)],[57]) ).
thf(30,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(649,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)],[30]) ).
thf(306,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(1690,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)],[306]) ).
thf(387,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(2065,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)],[387]) ).
thf(350,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(1894,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)],[350]) ).
thf(491,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(2493,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)],[491]) ).
thf(72,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(784,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)],[72]) ).
thf(526,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(2637,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(471,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(2422,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)],[471]) ).
thf(365,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(1969,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)],[365]) ).
thf(209,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(1307,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)],[209]) ).
thf(298,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(1667,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)],[298]) ).
thf(345,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(1877,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)],[345]) ).
thf(64,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(758,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ( 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 )
<=> ( ( ~ ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A @ ( v_h____ @ hAPP ) )
!= v_n____ )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ 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 ) )
& ( ( ( A @ ( v_h____ @ hAPP ) )
= v_n____ )
=> ( v_e____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ 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 ) ) ) )
& ( ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ 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',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ( 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 )
<=> ( ( ~ ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A @ ( v_h____ @ hAPP ) )
!= v_n____ )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ 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 ) )
& ( ( ( A @ ( v_h____ @ hAPP ) )
= v_n____ )
=> ( v_e____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ 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 ) ) ) )
& ( ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ 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(neg_conjecture,[status(cth)],[1]) ).
thf(535,plain,
~ ! [A: $i] :
( ( ( ( ~ ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A @ ( v_h____ @ hAPP ) )
!= v_n____ )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ 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 ) )
& ( ( ( A @ ( v_h____ @ hAPP ) )
= v_n____ )
=> ( v_e____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ 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 ) ) ) )
& ( ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ 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 ) ) )
=> ( A @ ( 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 ) )
& ( ( A @ ( 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 )
=> ( ( ~ ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A @ ( v_h____ @ hAPP ) )
!= v_n____ )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ hAPP ) @ 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 ) )
& ( ( ( A @ ( v_h____ @ hAPP ) )
= v_n____ )
=> ( v_e____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Oabove @ hAPP ) @ hAPP ) @ 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 ) ) ) )
& ( ( v_n____ @ ( A @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_e____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Omktop @ hAPP ) @ 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)],[2]) ).
thf(81,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(816,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)],[81]) ).
thf(217,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(1325,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)],[217]) ).
thf(119,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(964,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)],[119]) ).
thf(106,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(915,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)],[106]) ).
thf(20,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(609,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)],[20]) ).
thf(399,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(2111,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)],[399]) ).
thf(334,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(1821,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)],[334]) ).
thf(16,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(594,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)],[16]) ).
thf(77,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(799,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(354,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(1909,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)],[354]) ).
thf(169,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(1162,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)],[169]) ).
thf(480,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(2446,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)],[480]) ).
thf(23,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(621,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)],[23]) ).
thf(519,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(2593,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)],[519]) ).
thf(129,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(1029,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)],[129]) ).
thf(264,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(1556,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)],[264]) ).
thf(69,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(769,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(505,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(2542,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)],[505]) ).
thf(529,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(2647,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(515,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(2578,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)],[515]) ).
thf(305,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(1688,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)],[305]) ).
thf(87,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(827,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)],[87]) ).
thf(406,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(2139,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(466,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(2369,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)],[466]) ).
thf(323,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(1775,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)],[323]) ).
thf(246,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(1477,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)],[246]) ).
thf(502,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(2535,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)],[502]) ).
thf(32,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(653,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)],[32]) ).
thf(389,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(2069,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)],[389]) ).
thf(267,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(1562,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)],[267]) ).
thf(117,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(959,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)],[117]) ).
thf(416,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(2171,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)],[416]) ).
thf(139,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(1066,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)],[139]) ).
thf(525,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(2620,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)],[525]) ).
thf(143,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(1076,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)],[143]) ).
thf(52,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
thf(722,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(394,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(2096,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)],[394]) ).
thf(343,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(1873,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)],[343]) ).
thf(170,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(1166,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)],[170]) ).
thf(113,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(944,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)],[113]) ).
thf(444,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2271,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(34,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(663,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)],[34]) ).
thf(109,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(927,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)],[109]) ).
thf(199,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(1277,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)],[199]) ).
thf(61,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(749,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)],[61]) ).
thf(21,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(617,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)],[21]) ).
thf(220,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(1340,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)],[220]) ).
thf(521,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(2597,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)],[521]) ).
thf(173,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(1181,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)],[173]) ).
thf(516,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(2582,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)],[516]) ).
thf(132,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(1049,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)],[132]) ).
thf(179,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(1208,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)],[179]) ).
thf(14,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(589,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)],[14]) ).
thf(459,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 ) ) )
& ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
thf(2333,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 ) ) )
& ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(127,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(1018,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)],[127]) ).
thf(439,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(2256,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)],[439]) ).
thf(510,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(2564,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)],[510]) ).
thf(42,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(690,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)],[42]) ).
thf(128,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(1025,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)],[128]) ).
thf(534,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(2661,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)],[534]) ).
thf(47,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(705,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)],[47]) ).
thf(314,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(1743,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)],[314]) ).
thf(407,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(2143,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)],[407]) ).
thf(58,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(739,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)],[58]) ).
thf(149,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(1098,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(261,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(1547,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)],[261]) ).
thf(316,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(1748,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)],[316]) ).
thf(49,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(712,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)],[49]) ).
thf(4,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(557,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(322,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(1770,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)],[322]) ).
thf(424,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(2192,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)],[424]) ).
thf(100,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(887,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)],[100]) ).
thf(134,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(1053,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)],[134]) ).
thf(413,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(2165,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)],[413]) ).
thf(74,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(791,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)],[74]) ).
thf(12,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(585,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)],[12]) ).
thf(474,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(2429,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)],[474]) ).
thf(431,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(2219,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)],[431]) ).
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 ) ) ) )
=> ( ( 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(1763,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)],[320]) ).
thf(260,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(1538,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)],[260]) ).
thf(182,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(1218,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)],[182]) ).
thf(183,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(1220,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(105,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(907,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)],[105]) ).
thf(312,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(1716,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)],[312]) ).
thf(482,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(2454,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)],[482]) ).
thf(226,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(1358,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)],[226]) ).
thf(492,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(2500,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)],[492]) ).
thf(330,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(1802,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)],[330]) ).
thf(309,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1702,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(366,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(1972,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)],[366]) ).
thf(254,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(1504,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)],[254]) ).
thf(380,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(2030,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)],[380]) ).
thf(8,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(571,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(230,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(1372,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)],[230]) ).
thf(285,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(1617,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)],[285]) ).
thf(400,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(2113,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)],[400]) ).
thf(46,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(703,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(473,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(2426,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)],[473]) ).
thf(370,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(1981,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)],[370]) ).
thf(184,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(1221,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)],[184]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1284,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(447,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(2279,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)],[447]) ).
thf(17,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(600,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)],[17]) ).
thf(274,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(1585,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(162,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(1140,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)],[162]) ).
thf(356,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(1940,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)],[356]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
thf(1316,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_COMBK ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ofold__image ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nitpick_Orefl_H ) )
<=> ! [C: $i] : ( A @ ( C @ ( C @ ( 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_Nitpick_Orefl_H__def) ).
thf(2479,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nitpick_Orefl_H ) ) )
& ( ( A @ ( B @ c_Nitpick_Orefl_H ) )
=> ! [C: $i] : ( A @ ( C @ ( C @ ( 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)],[487]) ).
thf(393,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(2088,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)],[393]) ).
thf(364,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(1966,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)],[364]) ).
thf(304,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(1685,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)],[304]) ).
thf(215,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(1321,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)],[215]) ).
thf(453,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(2310,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)],[453]) ).
thf(294,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(1654,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)],[294]) ).
thf(65,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(759,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)],[65]) ).
thf(422,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(2187,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)],[422]) ).
thf(339,axiom,
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',fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096) ).
thf(1866,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)],[339]) ).
thf(326,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(1781,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)],[326]) ).
thf(181,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(1216,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)],[181]) ).
thf(125,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(1010,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)],[125]) ).
thf(236,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(1390,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)],[236]) ).
thf(203,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(1289,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)],[203]) ).
thf(433,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(2226,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)],[433]) ).
thf(198,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(1276,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(414,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(2167,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)],[414]) ).
thf(417,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(2174,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)],[417]) ).
thf(395,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(2098,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)],[395]) ).
thf(137,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(1062,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)],[137]) ).
thf(31,axiom,
tc_HOL_Obool @ class_Orderings_Otop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(652,plain,
tc_HOL_Obool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(376,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(2004,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)],[376]) ).
thf(315,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(1745,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)],[315]) ).
thf(28,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(632,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)],[28]) ).
thf(193,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(1244,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)],[193]) ).
thf(469,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(2416,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)],[469]) ).
thf(195,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(1253,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)],[195]) ).
thf(44,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(699,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)],[44]) ).
thf(114,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(946,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)],[114]) ).
thf(151,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(1101,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)],[151]) ).
thf(257,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(1523,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)],[257]) ).
thf(402,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(2130,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)],[402]) ).
thf(265,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(1558,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)],[265]) ).
thf(440,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(2262,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)],[440]) ).
thf(483,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(2462,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)],[483]) ).
thf(176,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(1193,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)],[176]) ).
thf(463,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(2362,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)],[463]) ).
thf(67,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(763,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)],[67]) ).
thf(296,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(1661,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)],[296]) ).
thf(530,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(2648,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)],[530]) ).
thf(324,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(1777,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)],[324]) ).
thf(89,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(832,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)],[89]) ).
thf(40,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(684,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)],[40]) ).
thf(434,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(2230,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)],[434]) ).
thf(448,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(2294,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)],[448]) ).
thf(210,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(1309,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)],[210]) ).
thf(159,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(1133,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)],[159]) ).
thf(451,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(2302,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)],[451]) ).
thf(200,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(1280,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)],[200]) ).
thf(91,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(835,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)],[91]) ).
thf(186,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(1229,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)],[186]) ).
thf(286,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(1625,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)],[286]) ).
thf(82,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(818,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)],[82]) ).
thf(231,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(1380,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)],[231]) ).
thf(208,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(1303,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)],[208]) ).
thf(318,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(1757,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)],[318]) ).
thf(56,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(735,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(123,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(999,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)],[123]) ).
thf(22,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(620,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(396,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(2102,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)],[396]) ).
thf(62,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(752,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)],[62]) ).
thf(271,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(1578,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)],[271]) ).
thf(360,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(1957,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)],[360]) ).
thf(90,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(833,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)],[90]) ).
thf(120,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(967,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)],[120]) ).
thf(259,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(1527,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)],[259]) ).
thf(166,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(1148,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)],[166]) ).
thf(301,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(1673,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)],[301]) ).
thf(212,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(1314,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)],[212]) ).
thf(250,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(1495,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)],[250]) ).
thf(295,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(1657,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(238,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(1410,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)],[238]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(2366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(116,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(955,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)],[116]) ).
thf(76,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(796,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)],[76]) ).
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_not__less0) ).
thf(2223,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(29,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(635,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)],[29]) ).
thf(386,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(2063,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)],[386]) ).
thf(282,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(1610,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)],[282]) ).
thf(55,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(728,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)],[55]) ).
thf(410,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(2159,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)],[410]) ).
thf(368,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(1977,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)],[368]) ).
thf(262,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1550,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(85,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(822,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)],[85]) ).
thf(277,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(1597,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)],[277]) ).
thf(206,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(1299,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)],[206]) ).
thf(346,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(1885,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)],[346]) ).
thf(97,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(871,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)],[97]) ).
thf(443,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(2270,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(467,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(2372,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)],[467]) ).
thf(190,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(1236,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)],[190]) ).
thf(493,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(2502,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)],[493]) ).
thf(475,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(2430,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)],[475]) ).
thf(196,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(1268,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)],[196]) ).
thf(233,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(1384,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)],[233]) ).
thf(488,axiom,
v_c____ != v_d____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096) ).
thf(2485,plain,
v_c____ != v_d____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(273,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(1582,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)],[273]) ).
thf(441,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(2265,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)],[441]) ).
thf(252,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(1500,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)],[252]) ).
thf(53,axiom,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
thf(723,plain,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(280,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(1606,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)],[280]) ).
thf(456,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(2321,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)],[456]) ).
thf(476,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(2436,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)],[476]) ).
thf(177,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(1204,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)],[177]) ).
thf(484,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(2470,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)],[484]) ).
thf(141,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(1069,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)],[141]) ).
thf(48,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(708,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)],[48]) ).
thf(477,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(2438,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)],[477]) ).
thf(449,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(2297,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)],[449]) ).
thf(71,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(775,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)],[71]) ).
thf(355,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(1917,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)],[355]) ).
thf(63,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(755,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(461,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(2351,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)],[461]) ).
thf(147,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(1088,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)],[147]) ).
thf(126,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(1014,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)],[126]) ).
thf(342,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(1870,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)],[342]) ).
thf(2731,plain,
$false,
inference(e,[status(thm)],[2199,1586,1337,1369,2341,1767,1995,846,1899,2595,962,2559,941,2331,555,1554,2163,892,628,1031,666,1295,1750,1068,2659,2527,1569,1142,1486,1158,2512,1692,677,1497,1671,1608,1137,2607,2035,1867,1233,1327,1640,1954,930,2575,2476,698,898,1835,2020,1650,1386,2067,2531,1887,2491,1782,885,1046,565,1366,2136,1703,1628,1287,2328,1792,1760,802,2185,2488,949,1055,724,2444,1860,2217,587,1323,1511,917,702,2420,559,2169,1479,1741,2520,1875,2049,2552,1319,1890,606,1347,1572,2178,1714,591,2650,1682,1677,1960,1183,2017,1489,2237,2105,1811,1109,1632,1418,2451,623,1858,2122,574,2254,1051,821,687,1072,660,2002,1345,1943,1600,1521,2205,2586,1975,602,766,1896,877,2190,1119,2424,1104,849,1863,1206,678,793,925,2364,761,1470,2232,2641,2000,714,1868,2589,894,746,1123,2147,1502,630,788,2132,1238,1560,1274,2441,1343,2560,2277,1355,1580,1174,2133,2032,815,1423,1602,1365,625,852,1178,1819,2179,1079,682,2313,583,2609,830,2653,1106,1234,1953,1804,2359,1064,1425,2537,2268,989,1397,1082,1964,933,1461,2080,1214,2108,2085,1612,1155,1414,2053,1889,1644,837,1099,2519,1297,2304,1382,1231,1131,2566,1984,1002,1979,2006,721,2203,1086,1779,2208,1695,1466,2645,2617,2529,1241,2546,1187,674,2408,1663,2235,1906,1135,1251,2176,1146,1959,824,2570,856,1301,2524,2275,2149,819,2048,1125,2525,772,1388,743,577,562,904,1615,1784,2161,1312,1635,1058,1997,1092,804,2474,2193,1669,1638,1224,2573,2319,979,2538,2084,1574,1524,1349,1589,2299,1144,737,649,1690,2065,1894,2493,784,2637,2422,1969,1307,1667,1877,758,535,816,1325,964,915,609,2111,1821,594,799,1909,1162,2446,621,2593,1029,1556,769,2542,2647,2578,1688,827,2139,2369,1775,1477,2535,653,2069,1562,959,2171,1066,2620,1076,722,2096,1873,1166,944,2271,663,927,1277,749,617,1340,2597,1181,2582,1049,1208,589,2333,1018,2256,2564,690,1025,2661,705,1743,2143,739,1098,1547,1748,712,557,1770,2192,887,1053,2165,791,585,2429,2219,1763,1538,1218,1220,907,1716,2454,1358,2500,1802,1702,1972,1504,2030,571,1372,1617,2113,703,2426,1981,1221,1284,2279,600,1585,1140,1940,1316,2479,2088,1966,1685,1321,2310,1654,759,2187,1866,1781,1216,1010,1390,1289,2226,1276,2167,2174,2098,1062,652,2004,1745,632,1244,2416,1253,699,946,1101,1523,2130,1558,2262,2462,1193,2362,763,1661,2648,1777,832,684,2230,2294,1309,1133,2302,1280,835,1229,1625,818,1380,1303,1757,735,999,620,2102,752,1578,1957,833,967,1527,1148,1673,1314,1495,1657,1410,2366,955,796,2223,635,2063,1610,728,2159,1977,1550,822,1597,1299,1885,871,2270,2372,1236,2502,2430,1268,1384,2485,1582,2265,1500,723,1606,2321,2436,1204,2470,1069,708,2438,2297,775,1917,755,2351,1088,1014,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT163+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 06:35:49 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.40 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.37/1.41 % [INFO] Parsing done (418ms).
% 2.37/1.43 % [INFO] Running in sequential loop mode.
% 3.28/1.82 % [INFO] eprover registered as external prover.
% 3.28/1.82 % [INFO] Scanning for conjecture ...
% 3.98/2.09 % [INFO] Found a conjecture (or negated_conjecture) and 532 axioms. Running axiom selection ...
% 5.25/2.32 % [INFO] Axiom selection finished. Selected 532 axioms (removed 0 axioms).
% 6.18/2.58 % [INFO] Problem is first-order (TPTP FOF).
% 6.64/2.61 % [INFO] Type checking passed.
% 6.64/2.61 % [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 ...
% 32.63/8.39 % External prover 'e' found a proof!
% 32.63/8.39 % [INFO] Killing All external provers ...
% 32.63/8.40 % Time passed: 7854ms (effective reasoning time: 6962ms)
% 32.63/8.40 % 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)>
% 33.12/8.41 % Axioms used in derivation (532): fact_add__le__less__mono, fact_xt1_I1_J, fact_le__SucI, fact_Pi__I, fact_insertCI, fact_nat_Osimps_I3_J, 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_pos__add__strict, fact_n_I2_J, fact_add__strict__right__mono, fact_Ints__odd__nonzero, fact_less__eq__nat_Osimps_I2_J, fact_inj__imp__surj__inv, fact_subset__UNIV, fact_inv__into__into, fact_insert__iff, fact_le__eq__less__or__eq, fact_surjh, fact_xt1_I4_J, fact_unanimity__def, fact_trans__less__add1, fact_injD, 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_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_folding__image__simple_Oeq__fold__g, 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, help_c__fFalse__1, 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_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_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_card__def, 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_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_Nitpick_Orefl_H__def, fact_inv__into__injective, 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_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_nat__case__Suc, 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_card_Oeq__fold__g, 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_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_list_Osimps_I4_J, fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096, 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_surj__imp__inj__inv, 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_Suc__lessI, fact_add__Suc__right, fact_const__Lin__Prof, fact_UNIV__Plus__UNIV
% 33.12/8.41 % No. of inferences in proof: 1068
% 33.12/8.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7854 ms resp. 6962 ms w/o parsing
% 37.42/9.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.42/9.30 % [INFO] Killing All external provers ...
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