TSTP Solution File: SCT164+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:50:52 EDT 2023
% Result : Theorem 20.48s 5.86s
% Output : Refutation 21.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 631
% Syntax : Number of formulae : 1166 ( 241 unt; 98 typ; 0 def)
% Number of atoms : 3150 ( 773 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 26296 ( 334 ~; 71 |; 264 &;23880 @)
% ( 129 <=>;1618 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 151 ( 151 >; 0 *; 0 +; 0 <<)
% Number of symbols : 100 ( 98 usr; 25 con; 0-6 aty)
% Number of variables : 3128 ( 0 ^;3094 !; 34 ?;3128 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_member_type,type,
c_member: $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(v_c_____type,type,
v_c____: $i ).
thf(v_d_____type,type,
v_d____: $i ).
thf(v_F_type,type,
v_F: $i ).
thf(v_P_____type,type,
v_P____: $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i ).
thf(c_If_type,type,
c_If: $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(v_h_____type,type,
v_h____: $i ).
thf(v_n_____type,type,
v_n____: $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i ).
thf(v_e_____type,type,
v_e____: $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_type,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(tc_sum_type,type,
tc_sum: $i > $i > $i ).
thf(c_Sum__Type_OPlus_type,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_b_____type,type,
v_b____: $i ).
thf(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple_type,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_FuncSet_OPi_type,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(v_Lab_____type,type,
v_Lab____: $i ).
thf(v_Lba_____type,type,
v_Lba____: $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OProf_type,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple__idem_type,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_Hilbert__Choice_Oinv__into_type,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(c_Int_Oring__1__class_OInts_type,type,
c_Int_Oring__1__class_OInts: $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__case_type,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Odictator_type,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_type,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_fFalse_type,type,
c_fFalse: $i ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(c_Wellfounded_Omax__extp_type,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(c_Wellfounded_Omax__ext_type,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_type,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(c_Wellfounded_Ofinite__psubset_type,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_Nat_Onat_Onat__size_type,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(c_Wellfounded_Omeasure_type,type,
c_Wellfounded_Omeasure: $i > $i > $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(1411,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( c_Set_Oinsert @ G @ A @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(629,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( c_Set_Oinsert @ G @ A @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(1190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(1633,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(1105,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( B != A )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ ( c_Set_Oimage @ A @ B @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(893,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ ( c_Set_Oimage @ A @ B @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(2427,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) )
=> ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(1818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1549,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(1110,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(515,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(2452,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
<=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(1024,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ( c_Fun_Oinj__on @ E @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
thf(1469,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ( c_Fun_Oinj__on @ E @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(1168,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2306,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(2131,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(256,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1454,plain,
~ ( hBOOL @ c_fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(1158,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(136,axiom,
! [A: $i] :
( ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ A )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(1005,plain,
! [A: $i] :
( ( ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ A )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) ) )
=> ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(2104,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(364,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(1882,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(1808,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(1544,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(179,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(1142,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(1041,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(1855,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1200,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
<=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) )
& ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(291,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
<=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1569,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_OIIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
thf(878,plain,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(655,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oimage @ C @ C @ A @ B ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ C @ A @ B )
=> ( ( c_Set_Oimage @ C @ C @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(1608,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oimage @ C @ C @ A @ B ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ C @ A @ B )
=> ( ( c_Set_Oimage @ C @ C @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(177,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ A )
=> ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).
thf(1137,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ A )
=> ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).
thf(550,plain,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(2184,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(56,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(715,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2141,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(1640,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(437,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(2146,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(391,axiom,
! [A: $i] :
( ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A )
= ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(1988,plain,
! [A: $i] :
( ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A )
= ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2459,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
thf(1507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( c_Set_Oimage @ F @ E @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( c_Set_Oimage @ F @ E @ C @ D ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).
thf(1222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( c_Set_Oimage @ F @ E @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( c_Set_Oimage @ F @ E @ C @ D ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(1095,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(2216,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(97,axiom,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Int_Oring__1__class_OInts @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__1) ).
thf(885,plain,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Int_Oring__1__class_OInts @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(2082,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(2516,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(279,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(1529,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(1803,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1265,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(38,axiom,
c_Fun_Oinj__on @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injh) ).
thf(651,plain,
c_Fun_Oinj__on @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).
thf(565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
thf(1366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(1628,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(241,axiom,
( c_Arrow__Order__Mirabelle_OProf
= ( c_FuncSet_OPi @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Prof__def) ).
thf(1409,plain,
( c_Arrow__Order__Mirabelle_OProf
= ( c_FuncSet_OPi @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(1871,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(934,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) )
& ( ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(1462,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
thf(949,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(312,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_Lab____ ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).
thf(1660,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_Lab____ ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( ( c_Finite__Set_Ofinite @ C @ A )
=> ( c_Finite__Set_Ofinite @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(1298,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( ( c_Finite__Set_Ofinite @ C @ A )
=> ( c_Finite__Set_Ofinite @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(2420,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(290,axiom,
class_Orderings_Otop @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(1568,plain,
class_Orderings_Otop @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__eq) ).
thf(2024,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(2169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2403,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(1087,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(1741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
thf(881,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(2007,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(460,axiom,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ v_Lba____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(2237,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ v_Lba____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(924,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(477,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(2324,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(789,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ C ) ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(343,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(1811,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(1373,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(520,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
thf(2469,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(623,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(1858,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(182,axiom,
! [A: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_Option_Ooption @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_Option_Ooption @ A ) @ tc_HOL_Obool ) ) )
<=> ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
thf(1151,plain,
! [A: $i] :
( ( ( c_Finite__Set_Ofinite @ ( tc_Option_Ooption @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_Option_Ooption @ A ) @ tc_HOL_Obool ) ) )
=> ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
& ( ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
=> ( c_Finite__Set_Ofinite @ ( tc_Option_Ooption @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_Option_Ooption @ A ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(400,axiom,
! [A: $i] :
( ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ A )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(2017,plain,
! [A: $i] :
( ( ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ A )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(192,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1183,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(418,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ v_Lab____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(2073,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ v_Lab____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ B )
!= ( hAPP @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(1051,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ B )
!= ( hAPP @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(81,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(821,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ C @ A ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(2508,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ C @ A ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(412,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ v_n____ ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I1_J) ).
thf(2058,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ v_n____ ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).
thf(734,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(2530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ C ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
thf(1351,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ C ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(660,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
thf(2242,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) )
=> ( ( B != A )
& ( ( A = E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__comp) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(239,axiom,
( ( c_Set_Oimage @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjh) ).
thf(1405,plain,
( ( c_Set_Oimage @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1600,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
=> ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(849,plain,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
=> ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Set_Oimage @ F @ E @ D @ C )
= B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( c_Set_Oimage @ F @ E @ D @ ( c_Set_Oimage @ E @ F @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
thf(1521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Set_Oimage @ F @ E @ D @ C )
= B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( c_Set_Oimage @ F @ E @ D @ ( c_Set_Oimage @ E @ F @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(453,axiom,
class_Finite__Set_Ofinite @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(2205,plain,
class_Finite__Set_Ofinite @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(170,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1119,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(489,axiom,
v_c____ != v_d____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096) ).
thf(2371,plain,
v_c____ != v_d____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Set_Oimage @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Set_Oimage @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(2364,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(69,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
<=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(761,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(408,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2047,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(1868,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(2232,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(2296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(1730,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
thf(1163,plain,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(499,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(2409,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(910,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(120,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ v_n____ ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ A ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I2_J) ).
thf(957,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ v_n____ ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ A ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(746,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(1343,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(1021,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(952,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(1519,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(1824,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(729,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(533,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ A ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) @ c_Arrow__Order__Mirabelle_OProf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiProf) ).
thf(2528,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ A ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) @ c_Arrow__Order__Mirabelle_OProf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(2396,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(2015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1174,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Wellfounded_Omeasure @ D @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
thf(2133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Wellfounded_Omeasure @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Wellfounded_Omeasure @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(202,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1217,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(438,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2147,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( class_Int_Oring__char__0 @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Int_Oring__1__class_OInts @ B ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
thf(1602,plain,
! [A: $i,B: $i] :
( ( class_Int_Oring__char__0 @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Int_Oring__1__class_OInts @ B ) ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(287,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1555,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(1951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(665,plain,
! [A: $i,B: $i] :
( ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1624,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(2200,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Finite__Set_Ofinite @ D @ C )
& ( c_Finite__Set_Ofinite @ B @ A ) )
=> ( ( c_Finite__Set_Ocard @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ D @ C ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) ) )
& ( ~ ( ( c_Finite__Set_Ofinite @ D @ C )
& ( c_Finite__Set_Ofinite @ B @ A ) )
=> ( ( c_Finite__Set_Ocard @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
thf(1836,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Finite__Set_Ofinite @ D @ C )
& ( c_Finite__Set_Ofinite @ B @ A ) )
=> ( ( c_Finite__Set_Ocard @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ D @ C ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) ) )
& ( ~ ( ( c_Finite__Set_Ofinite @ D @ C )
& ( c_Finite__Set_Ofinite @ B @ A ) )
=> ( ( c_Finite__Set_Ocard @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Set_Oimage @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff__all) ).
thf(1210,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Set_Oimage @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D ) )
& ( ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D )
=> ( ( c_Set_Oimage @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(1407,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ D @ B @ E @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ D @ C ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
thf(2313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ D @ B @ E @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ D @ C ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ D @ C ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
=> ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ D @ B @ E @ C ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(234,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_F ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(1392,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_F ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(710,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(1910,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(974,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) @ A ) )
=> ( ( c_Finite__Set_Ofinite @ D @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ E @ B ) ) @ ( c_Finite__Set_Ocard @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(1012,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) @ A ) )
=> ( ( c_Finite__Set_Ofinite @ D @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ E @ B ) ) @ ( c_Finite__Set_Ocard @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( c_Finite__Set_Ocard @ C @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(916,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( c_Finite__Set_Ocard @ C @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_fun @ A @ C ) @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ A @ C ) @ D @ ( c_COMBK @ C @ A ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__fun) ).
thf(2445,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_fun @ A @ C ) @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ A @ C ) @ D @ ( c_COMBK @ C @ A ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(1938,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(847,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(99,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(889,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(2179,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(225,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(1360,plain,
class_Orderings_Opreorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(1089,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(356,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(1851,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(491,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B ) @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(2377,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B ) @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(1794,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
thf(615,plain,
! [A: $i,B: $i] :
( ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1375,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(153,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(1064,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(388,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(1970,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(980,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(246,axiom,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(1425,plain,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(321,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop ) @ v_P____ ) ) @ v_e____ ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove ) @ v_P____ ) ) @ v_c____ ) ) @ v_e____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot ) @ v_P____ ) ) @ v_e____ ) ) ) ) @ c_Arrow__Order__Mirabelle_OProf ),
file('/export/starexec/sandbox2/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(1719,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop ) @ v_P____ ) ) @ v_e____ ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove ) @ v_P____ ) ) @ v_c____ ) ) @ v_e____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot ) @ v_P____ ) ) @ v_e____ ) ) ) ) @ c_Arrow__Order__Mirabelle_OProf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) ) ) @ ( c_Finite__Set_Ocard @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) ) ) @ ( c_Finite__Set_Ocard @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).
thf(578,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(93,axiom,
( ( c_Finite__Set_Ocard @ tc_Product__Type_Ounit @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Product__Type_Ounit @ tc_HOL_Obool ) ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
thf(874,plain,
( ( c_Finite__Set_Ocard @ tc_Product__Type_Ounit @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Product__Type_Ounit @ tc_HOL_Obool ) ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(2115,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Nat_Onat_Onat__case @ C @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(1160,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Nat_Onat_Onat__case @ C @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(1082,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(1361,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).
thf(753,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(669,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(504,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2419,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(2455,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(376,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(1937,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2172,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(428,axiom,
! [A: $i] :
( ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Finite__Set_Ocard @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(2108,plain,
! [A: $i] :
( ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Finite__Set_Ocard @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ~ ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(1446,plain,
! [A: $i,B: $i] :
( ~ ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) )
=> ( ( ( c_Finite__Set_Ocard @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(1016,plain,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) )
=> ( ( ( c_Finite__Set_Ocard @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ C ) @ ( c_Sum__Type_OPlus @ D @ C @ B @ A ) )
=> ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
thf(590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ C ) @ ( c_Sum__Type_OPlus @ D @ C @ B @ A ) )
=> ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(1039,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(970,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(474,axiom,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
thf(2317,plain,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(547,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(837,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(2504,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(210,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(1263,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(2450,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(1451,plain,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(2482,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(1720,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(1525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1478,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(1249,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1539,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(257,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1456,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(2153,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(2387,plain,
! [A: $i,B: $i] :
( ( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(1831,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(174,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1131,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(40,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(654,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(2355,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(1192,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(519,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(2465,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(152,axiom,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/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(1060,plain,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(148,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(1050,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(23,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(605,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( D = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(235,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(1393,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(359,axiom,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(1857,plain,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( ( c_Set_Oimage @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(1991,plain,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( ( c_Set_Oimage @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(2203,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(633,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(406,axiom,
( ( c_Nat_Onat_Onat__size @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
thf(2043,plain,
( ( c_Nat_Onat_Onat__size @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(109,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(921,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(657,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B ) @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(1170,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B ) @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(274,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(1515,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(72,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(773,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ C @ A ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(1732,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ C @ A ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(1846,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ C ) @ D ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ C ) @ D ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
thf(1466,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(496,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_P____ @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) @ v_h____ ) @ v_n____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096) ).
thf(2402,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_P____ @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) @ v_h____ ) @ v_n____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(1135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( c_Set_Oinsert @ B @ ( hAPP @ A @ D ) @ ( c_Set_Oimage @ E @ B @ A @ C ) )
= ( c_Set_Oimage @ E @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
thf(1219,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( c_Set_Oinsert @ B @ ( hAPP @ A @ D ) @ ( c_Set_Oimage @ E @ B @ A @ C ) )
= ( c_Set_Oimage @ E @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Set_Oimage @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(1273,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Set_Oimage @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) ) )
& ( ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Set_Oimage @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( c_Finite__Set_Ofinite @ C @ ( c_Set_Oinsert @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(573,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( c_Finite__Set_Ofinite @ C @ ( c_Set_Oinsert @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ B @ A @ D ) ) @ ( c_Set_Oimage @ E @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
thf(1631,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ B @ A @ D ) ) @ ( c_Set_Oimage @ E @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
thf(601,plain,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(459,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(2235,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(2144,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(105,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(906,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(965,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(28,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(618,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(2413,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( c_Set_Oimage @ F @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(2292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( c_Set_Oimage @ F @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
thf(1959,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofinite @ E @ ( c_Set_Oimage @ D @ E @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( c_Finite__Set_Ofinite @ B @ ( c_Set_Oimage @ D @ B @ ( hAPP @ ( c_COMBB @ E @ B @ D @ A ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
thf(1103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofinite @ E @ ( c_Set_Oimage @ D @ E @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( c_Finite__Set_Ofinite @ B @ ( c_Set_Oimage @ D @ B @ ( hAPP @ ( c_COMBB @ E @ B @ D @ A ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(2028,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( c_Finite__Set_Ofinite @ D @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ E @ B ) ) @ ( c_Finite__Set_Ocard @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj) ).
thf(1595,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( c_Finite__Set_Ofinite @ D @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ E @ B ) ) @ ( c_Finite__Set_Ocard @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= ( c_Finite__Set_Ocard @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).
thf(562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( c_Finite__Set_Ocard @ C @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= ( c_Finite__Set_Ocard @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).
thf(1916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(457,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2225,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(843,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(301,axiom,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/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(1620,plain,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(1652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(1535,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Set_Oimage @ A @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
thf(1403,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Set_Oimage @ A @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(1124,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(1256,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBS @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(1488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBS @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ C ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ C @ D @ B ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).
thf(1139,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ C ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ C @ D @ B ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2326,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Int_Oring__1__class_OInts @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Int_Oring__1__class_OInts @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Int_Oring__1__class_OInts @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__add) ).
thf(1371,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Int_Oring__1__class_OInts @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Int_Oring__1__class_OInts @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Int_Oring__1__class_OInts @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(2442,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(1092,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(366,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(1897,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Set_Oimage @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ D @ C @ B @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
thf(1258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Set_Oimage @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ D @ C @ B @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_sum @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_sum @ B @ A ) @ tc_HOL_Obool ) ) )
<=> ( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
thf(2358,plain,
! [A: $i,B: $i] :
( ( ( c_Finite__Set_Ofinite @ ( tc_sum @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_sum @ B @ A ) @ tc_HOL_Obool ) ) )
=> ( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) )
& ( ( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( c_Finite__Set_Ofinite @ ( tc_sum @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_sum @ B @ A ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
<=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(540,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Groups_Oone__class_Oone @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
thf(611,plain,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oimage @ C @ C @ A @ B ) ) )
=> ( c_Fun_Oinj__on @ C @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(787,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oimage @ C @ C @ A @ B ) ) )
=> ( c_Fun_Oinj__on @ C @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(1464,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(947,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(528,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2510,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(2521,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(200,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(1209,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( c_Sum__Type_OPlus @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_sum @ B @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
thf(900,plain,
! [A: $i,B: $i] :
( ( c_Sum__Type_OPlus @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_sum @ B @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(2151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ A ) @ C ) @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(2084,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ A ) @ C ) @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(2415,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(784,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(147,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(1048,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(1542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ C ) @ ( c_Sum__Type_OPlus @ D @ C @ B @ A ) )
<=> ( ( c_Finite__Set_Ofinite @ D @ B )
& ( c_Finite__Set_Ofinite @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
thf(567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ C ) @ ( c_Sum__Type_OPlus @ D @ C @ B @ A ) )
=> ( ( c_Finite__Set_Ofinite @ D @ B )
& ( c_Finite__Set_Ofinite @ C @ A ) ) )
& ( ( ( c_Finite__Set_Ofinite @ D @ B )
& ( c_Finite__Set_Ofinite @ C @ A ) )
=> ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ C ) @ ( c_Sum__Type_OPlus @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(737,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(1122,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(387,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(1969,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(420,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2079,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2311,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(681,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1853,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(1349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(464,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096) ).
thf(2284,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( c_Set_Oimage @ C @ A @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( c_Set_Oimage @ C @ A @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) )
=> ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(1722,plain,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) )
=> ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(1144,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(649,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(146,axiom,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) )
=> ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ B ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) ) ),
file('/export/starexec/sandbox2/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(1043,plain,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) )
=> ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ B ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ ( c_Set_Oimage @ C @ D @ B @ A ) )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( c_Finite__Set_Ofinite @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(599,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ ( c_Set_Oimage @ C @ D @ B @ A ) )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( c_Finite__Set_Ofinite @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1439,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(1471,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(155,axiom,
! [A: $i,B: $i] : ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(1080,plain,
! [A: $i,B: $i] : ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(6,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(552,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop ) @ v_P____ ) ) @ v_e____ ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove ) @ v_P____ ) ) @ v_c____ ) ) @ v_e____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot ) @ v_P____ ) ) @ v_e____ ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop ) @ v_P____ ) ) @ v_e____ ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove ) @ v_P____ ) ) @ v_c____ ) ) @ v_e____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot ) @ v_P____ ) ) @ v_e____ ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(535,plain,
~ ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop ) @ v_P____ ) ) @ v_e____ ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove ) @ v_P____ ) ) @ v_c____ ) ) @ v_e____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot ) @ v_P____ ) ) @ v_e____ ) ) ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop ) @ v_P____ ) ) @ v_e____ ) ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal ) @ v_h____ ) ) @ v_n____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove ) @ v_P____ ) ) @ v_c____ ) ) @ v_e____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot ) @ v_P____ ) ) @ v_e____ ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(305,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ v_Lba____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(1630,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ v_Lba____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(621,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Set_Oimage @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
thf(2410,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Set_Oimage @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(1029,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(232,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
<=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(1381,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) ) )
& ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Ounanimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( class_Orderings_Otop @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(932,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( class_Orderings_Otop @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(167,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1112,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(314,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(1667,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(68,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(758,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(1821,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( class_Finite__Set_Ofinite @ B )
& ( class_Finite__Set_Ofinite @ A ) )
=> ( class_Finite__Set_Ofinite @ ( tc_sum @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
thf(594,plain,
! [A: $i,B: $i] :
( ( ( class_Finite__Set_Ofinite @ B )
& ( class_Finite__Set_Ofinite @ A ) )
=> ( class_Finite__Set_Ofinite @ ( tc_sum @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).
thf(1556,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1460,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1293,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(46,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ v_n____ ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I3_J) ).
thf(668,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ v_n____ ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(912,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(983,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
thf(959,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Set_Oimage @ F @ E @ D @ ( c_Set_Oimage @ C @ F @ B @ A ) )
= ( c_Set_Oimage @ C @ E @ ( hAPP @ ( c_COMBB @ F @ E @ C @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
thf(768,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Set_Oimage @ F @ E @ D @ ( c_Set_Oimage @ C @ F @ B @ A ) )
= ( c_Set_Oimage @ C @ E @ ( hAPP @ ( c_COMBB @ F @ E @ C @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(636,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ B @ E ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C3_C) ).
thf(1066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ B @ E ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( ( class_Finite__Set_Ofinite @ B )
& ( class_Finite__Set_Ofinite @ A ) )
=> ( class_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
thf(2064,plain,
! [A: $i,B: $i] :
( ( ( class_Finite__Set_Ofinite @ B )
& ( class_Finite__Set_Ofinite @ A ) )
=> ( class_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(24,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(608,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Set_Oimage @ F @ E @ D @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ F @ A @ B ) ) @ C ) )
=> ( ( c_Finite__Set_Ofinite @ F @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( c_Finite__Set_Ocard @ F @ C )
= ( c_Finite__Set_Ocard @ E @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij__eq) ).
thf(986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Set_Oimage @ F @ E @ D @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ F @ A @ B ) ) @ C ) )
=> ( ( c_Finite__Set_Ofinite @ F @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( c_Finite__Set_Ocard @ F @ C )
= ( c_Finite__Set_Ocard @ E @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Otop @ C )
=> ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
thf(1113,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Otop @ C )
=> ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(426,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2101,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ( hAPP @ C @ ( c_Set_Oinsert @ G @ A @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(851,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ G @ B )
=> ( ( hAPP @ C @ ( c_Set_Oinsert @ G @ A @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(110,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ A ) ) @ c_Arrow__Order__Mirabelle_OProf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
thf(922,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ A ) ) @ c_Arrow__Order__Mirabelle_OProf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ C @ A ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ C @ A ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ F ) ) @ A ) @ ( c_FuncSet_OPi @ E @ F @ B @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ E ) @ C ) ) ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( c_Finite__Set_Ofinite @ F @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( c_Finite__Set_Ocard @ F @ C )
= ( c_Finite__Set_Ocard @ E @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij) ).
thf(1396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ F ) ) @ A ) @ ( c_FuncSet_OPi @ E @ F @ B @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ E ) @ C ) ) ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( c_Finite__Set_Ofinite @ F @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( c_Finite__Set_Ocard @ F @ C )
= ( c_Finite__Set_Ocard @ E @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2439,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(395,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(2005,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(1626,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(461,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(2239,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(1166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(2318,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(1420,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(36,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(648,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(383,axiom,
c_Finite__Set_Ofinite @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__indi) ).
thf(1958,plain,
c_Finite__Set_Ofinite @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(410,axiom,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ v_Lab____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(2054,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ v_Lab____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(379,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(1948,plain,
class_Orderings_Oorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
thf(663,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ A @ C ) ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(2471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ A @ C ) ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(112,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(927,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2037,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(2513,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(2298,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(1003,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(872,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1368,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(1267,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(1531,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( c_Finite__Set_Ofinite @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
thf(1748,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( c_Finite__Set_Ofinite @ C @ A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( c_Finite__Set_Ofinite @ C @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ ( c_Set_Oinsert @ C @ B @ A ) )
<=> ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(580,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Finite__Set_Ofinite @ C @ ( c_Set_Oinsert @ C @ B @ A ) )
=> ( c_Finite__Set_Ofinite @ C @ A ) )
& ( ( c_Finite__Set_Ofinite @ C @ A )
=> ( c_Finite__Set_Ofinite @ C @ ( c_Set_Oinsert @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ D ) ) @ ( hAPP @ B @ F ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ D ) ) @ ( hAPP @ v_F @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C4_C) ).
thf(855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ D ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ F ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ D ) ) @ ( hAPP @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ D ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ D ) ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(705,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(298,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(1611,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(1156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(205,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_P____ @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ A ) ) @ v_n____ ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ ( hAPP @ v_P____ @ A ) ) @ v_e____ ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ A ) ) @ v_n____ ) )
=> ( ( ( ( hAPP @ v_h____ @ A )
= v_n____ )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ ( hAPP @ v_P____ @ A ) ) @ v_c____ ) @ v_e____ ) ) ) )
& ( ( ( hAPP @ v_h____ @ A )
!= v_n____ )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ ( hAPP @ v_P____ @ A ) ) @ v_e____ ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_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_092_060_094esub_062_Ad_J_096) ).
thf(1225,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_P____ @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ A ) ) @ v_n____ ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ ( hAPP @ v_P____ @ A ) ) @ v_e____ ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ A ) ) @ v_n____ ) )
=> ( ( ( ( hAPP @ v_h____ @ A )
= v_n____ )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ ( hAPP @ v_P____ @ A ) ) @ v_c____ ) @ v_e____ ) ) ) )
& ( ( ( hAPP @ v_h____ @ A )
!= v_n____ )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ ( hAPP @ v_P____ @ A ) ) @ v_e____ ) ) ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ A ) ) @ v_n____ ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ ( hAPP @ v_P____ @ A ) ) @ v_e____ ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ A ) ) @ v_n____ ) )
=> ( ( ( ( hAPP @ v_h____ @ A )
= v_n____ )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ ( hAPP @ v_P____ @ A ) ) @ v_c____ ) @ v_e____ ) ) ) )
& ( ( ( hAPP @ v_h____ @ A )
!= v_n____ )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ ( hAPP @ v_P____ @ A ) ) @ v_e____ ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_c____ ) @ v_d____ ) ) @ ( hAPP @ v_P____ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1743,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(2192,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(887,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(2012,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( c_Set_Oimage @ E @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(1711,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( c_Set_Oimage @ E @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(673,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( class_Int_Oring__char__0 @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Int_Oring__1__class_OInts @ B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
thf(1716,plain,
! [A: $i,B: $i] :
( ( class_Int_Oring__char__0 @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Int_Oring__1__class_OInts @ B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(249,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(1432,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C ) @ E ) @ D ) ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
thf(1300,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C ) @ E ) @ D ) ) )
=> ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C ) @ E ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Fun_Oinj__on @ D @ B @ A @ C )
<=> ( ( c_Finite__Set_Ocard @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) )
= ( c_Finite__Set_Ocard @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(585,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( ( c_Fun_Oinj__on @ D @ B @ A @ C )
=> ( ( c_Finite__Set_Ocard @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) )
= ( c_Finite__Set_Ocard @ D @ C ) ) )
& ( ( ( c_Finite__Set_Ocard @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) )
= ( c_Finite__Set_Ocard @ D @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
thf(2337,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
thf(1980,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Olinorder @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E ) @ B ) @ A ) )
=> ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ C )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ C @ B ) ) @ ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).
thf(1085,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ C @ B ) ) @ ( c_Finite__Set_Ocard @ C @ ( c_Set_Oinsert @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(1285,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(1188,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1186,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Int_Oring__1__class_OInts @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
thf(1898,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Int_Oring__1__class_OInts @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(2113,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(2379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(1955,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(247,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(1427,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(1504,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(2511,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ C ) @ ( c_Sum__Type_OPlus @ D @ C @ B @ A ) )
=> ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
thf(612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ ( tc_sum @ D @ C ) @ ( c_Sum__Type_OPlus @ D @ C @ B @ A ) )
=> ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(94,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(876,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(300,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(1617,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(525,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2500,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(744,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(1485,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ A ) )
& ( D
= ( c_Set_Oimage @ C @ E @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(1972,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ A ) )
& ( D
= ( c_Set_Oimage @ C @ E @ B @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ A ) )
& ( D
= ( c_Set_Oimage @ C @ E @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(407,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2045,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(1949,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(671,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Set_Oimage @ E @ D @ ( hAPP @ ( c_COMBB @ C @ D @ E @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Set_Oimage @ C @ D @ B @ ( c_Set_Oimage @ E @ C @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).
thf(903,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Set_Oimage @ E @ D @ ( hAPP @ ( c_COMBB @ C @ D @ E @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Set_Oimage @ C @ D @ B @ ( c_Set_Oimage @ E @ C @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2194,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ~ ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).
thf(2209,plain,
! [A: $i,B: $i] :
( ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ~ ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(2187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(417,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
thf(2071,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
thf(1998,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(373,axiom,
~ ! [A: $i] :
( ( c_Fun_Oinj__on @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1918,plain,
~ ! [A: $i] :
( ( c_Fun_Oinj__on @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Finite__Set_Ocard @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(1649,plain,
! [A: $i,B: $i] :
( ( c_Finite__Set_Ofinite @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Finite__Set_Ocard @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(157,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1084,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Nat_Onat @ B ) ) ) ) )
=> ( B
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Nat_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
thf(2347,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Nat_Onat @ B ) ) ) ) )
=> ( B
= ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Nat_Onat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( c_Set_Oimage @ E @ D @ C @ B )
= ( c_Set_Oimage @ E @ D @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(1654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( ( c_Set_Oimage @ E @ D @ C @ B )
= ( c_Set_Oimage @ E @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Set_Oimage @ E @ D @ C @ B )
= ( c_Set_Oimage @ E @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(429,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(2110,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(1390,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(470,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P____ ) @ c_Arrow__Order__Mirabelle_OProf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
thf(2305,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P____ ) @ c_Arrow__Order__Mirabelle_OProf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(1734,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
| ( B = A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(341,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(1807,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ B ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ B @ C @ A ) ) @ ( c_FuncSet_OPi @ E @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
thf(771,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ B ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ B @ C @ A ) ) @ ( c_FuncSet_OPi @ E @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(122,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(961,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofinite @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) )
=> ( c_Finite__Set_Ofinite @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofinite @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) )
=> ( c_Finite__Set_Ofinite @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(2174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(1674,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__f) ).
thf(2406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(1481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(163,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(1101,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(39,axiom,
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(652,plain,
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(1745,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(731,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(781,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( c_Set_Oimage @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( c_Set_Oimage @ E @ D @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
thf(2447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( c_Set_Oimage @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( c_Set_Oimage @ E @ D @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(2009,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1491,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B ) @ A ) ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(1689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B ) @ A ) ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(2462,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(415,axiom,
! [A: $i] :
( ( c_Nat_Onat_Onat__size @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_Onat_Onat__size @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
thf(2066,plain,
! [A: $i] :
( ( c_Nat_Onat_Onat__size @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_Onat_Onat__size @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(1661,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(393,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1994,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(929,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(2330,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ D @ ( c_Set_Oimage @ C @ D @ B @ A ) ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
=> ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(2095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ D @ ( c_Set_Oimage @ C @ D @ B @ A ) ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
=> ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(832,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
thf(684,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(1614,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(800,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(1116,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(1133,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(999,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1512,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(469,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(2302,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1725,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(2385,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(2155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
thf(967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( ( class_Finite__Set_Ofinite @ B )
& ( class_Finite__Set_Ofinite @ A ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(835,plain,
! [A: $i,B: $i] :
( ( ( class_Finite__Set_Ofinite @ B )
& ( class_Finite__Set_Ofinite @ A ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1546,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(818,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(1593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(2050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(1757,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(22,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ A )
=> ( class_Finite__Set_Ofinite @ ( tc_Option_Ooption @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
thf(603,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ A )
=> ( class_Finite__Set_Ofinite @ ( tc_Option_Ooption @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(1436,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(219,axiom,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) )
& ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ B ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) ),
file('/export/starexec/sandbox2/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(1335,plain,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) )
& ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ B ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ v_h____ ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( c_Nitpick_Orefl_H @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(2366,plain,
! [A: $i,B: $i] :
( ( ( c_Nitpick_Orefl_H @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) )
=> ( c_Nitpick_Orefl_H @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Set_Oimage @ E @ D @ C @ ( c_Set_Oinsert @ E @ B @ A ) )
= ( c_Set_Oinsert @ D @ ( hAPP @ C @ B ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
thf(1197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Set_Oimage @ E @ D @ C @ ( c_Set_Oinsert @ E @ B @ A ) )
= ( c_Set_Oinsert @ D @ ( hAPP @ C @ B ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(2340,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(1816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).
thf(1172,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(897,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(503,axiom,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Int_Oring__1__class_OInts @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__0) ).
thf(2417,plain,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Int_Oring__1__class_OInts @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(484,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ B ) ) @ ( c_COMBI @ B ) ) @ ( c_FuncSet_OPi @ B @ B @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
thf(2353,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ B ) ) @ ( c_COMBI @ B ) ) @ ( c_FuncSet_OPi @ B @ B @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( ( c_Finite__Set_Ocard @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) )
= ( c_Finite__Set_Ocard @ D @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(596,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( ( c_Finite__Set_Ocard @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) )
= ( c_Finite__Set_Ocard @ D @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(140,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1019,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(1357,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(992,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(1713,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
thf(691,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(237,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1399,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ D @ C ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).
thf(2138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ B @ A )
=> ( ( c_Finite__Set_Ocard @ ( tc_sum @ D @ B ) @ ( c_Sum__Type_OPlus @ D @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Finite__Set_Ocard @ D @ C ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(1129,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oimage @ E @ D @ C @ A ) ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1827,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( c_Finite__Set_Ofinite @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(1261,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( c_Finite__Set_Ofinite @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1500,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
thf(1923,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ! [G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ A @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ B @ G ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ F ) @ E ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(723,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(1597,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(1880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(2484,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(1885,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ C @ B ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(2321,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Finite__Set_Ofinite @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Finite__Set_Ocard @ C @ B ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(1962,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nat_Onat_Onat__case @ D @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(2206,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nat_Onat_Onat__case @ D @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(2074,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(509,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_Lba____ ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).
thf(2438,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_Lba____ ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(2087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Set_Oimage @ C @ E @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( c_Finite__Set_Ofinite @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( c_Finite__Set_Ofinite @ B @ ( c_Set_Oimage @ D @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oinsert @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(1912,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( c_Set_Oinsert @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(1848,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
<=> ( hBOOL @ ( c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
thf(2059,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B ) @ A ) ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1769,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B ) @ A ) ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(755,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(1449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).
thf(1812,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(1014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( c_Finite__Set_Ofinite @ F @ A )
=> ( ( hAPP @ B @ A )
= ( c_Finite__Set_Ofold__image @ G @ F @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(1417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( c_Finite__Set_Ofinite @ F @ A )
=> ( ( hAPP @ B @ A )
= ( c_Finite__Set_Ofold__image @ G @ F @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(972,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(2546,plain,
$false,
inference(e,[status(thm)],[1411,629,1190,1633,1105,893,2427,555,1818,1549,1110,2452,809,1024,1469,1168,2306,2131,1454,1158,1005,2104,1882,1808,1544,1142,1041,1855,1200,1422,1569,878,655,1608,1137,550,2184,715,2141,1640,2146,1988,2459,1507,1222,1095,2216,885,2082,2516,1529,1803,1265,651,2432,1914,565,1366,1628,1409,2039,1871,934,1462,949,1660,1298,2420,638,1568,2024,2169,2403,1087,1741,881,2007,2237,924,2324,789,1811,1373,2469,623,1858,1151,2017,1183,2073,1051,821,2508,2058,687,734,2530,1351,660,2242,1433,1405,1600,849,1521,2205,1119,2371,1206,2473,2364,761,2047,1868,2232,2296,1730,1057,1163,2409,910,957,746,1343,1021,952,1519,2277,1824,729,2528,2396,2015,1174,1676,2133,1217,2147,1602,1555,1951,665,1624,2200,1836,1210,1407,2313,1392,710,1910,974,1012,916,2445,1938,847,889,2179,1360,1089,1762,1851,2377,1794,615,1375,1064,1970,725,980,1425,1719,869,989,2300,578,874,2115,1160,1082,1361,753,669,2419,2455,1937,1791,2172,2108,1446,1016,590,1039,970,2317,547,837,2504,1263,2450,1451,1429,2482,1720,1525,1478,1249,1539,1456,2153,2387,1831,1131,654,2355,1192,2465,1060,1050,605,1759,1393,1857,1991,2203,633,2043,921,657,1170,1515,773,2423,1732,1846,1054,1466,2402,1135,1219,1273,573,1631,601,2235,2144,906,965,1727,618,2413,1754,2292,1959,1103,2028,1595,562,1833,1916,2225,843,1620,1652,1535,1403,1965,1124,1256,1488,1139,2326,1371,2442,1092,1897,1258,2358,540,611,787,1464,947,2510,2521,1209,900,2151,2084,2415,784,1048,1542,567,737,1122,1969,2079,2311,681,1853,1349,2097,2284,1933,1722,1144,649,1043,599,1439,1471,1080,552,535,1630,621,2410,1029,626,943,1381,932,1112,890,1667,758,1339,1821,594,1556,1460,1293,668,912,983,2350,959,768,636,1066,2064,608,986,1113,2101,851,922,2069,1396,2439,2005,1626,2239,1166,2318,1420,648,1958,2054,1948,663,2471,927,2037,2513,2298,1003,872,1941,1368,1267,1531,776,1748,580,855,705,1611,1156,1225,1743,2192,887,1566,2012,1711,673,1716,1432,1300,585,2337,1980,1901,1085,1285,1188,1186,2056,1898,2113,2379,1955,1427,1504,2511,612,876,1617,2500,744,1485,1972,2045,1949,671,903,2194,2209,2187,1289,2071,1998,1918,1649,1084,2347,1654,2110,1390,2305,1734,1807,771,961,963,2174,1674,2406,1481,1101,652,1745,731,781,2447,2009,1491,1689,2041,2462,2066,1661,1994,929,2330,2095,832,684,716,1614,800,1116,1133,2374,999,1512,2302,1725,2385,2155,967,835,1546,818,1593,2050,1757,603,1527,1148,1436,1335,2366,1197,828,2340,1816,1495,1172,897,2417,2353,575,596,1019,1357,992,1713,691,1399,2138,1829,1129,1827,1261,1500,1923,723,1597,1880,2484,1885,2321,1962,2206,2074,2438,2087,592,1912,2177,1848,2059,1769,755,1449,1812,1014,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:59:41 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.97/1.20 % [INFO] Parsing done (318ms).
% 1.97/1.21 % [INFO] Running in sequential loop mode.
% 2.66/1.45 % [INFO] eprover registered as external prover.
% 2.76/1.46 % [INFO] cvc4 registered as external prover.
% 2.76/1.46 % [INFO] Scanning for conjecture ...
% 3.22/1.63 % [INFO] Found a conjecture and 532 axioms. Running axiom selection ...
% 4.03/1.79 % [INFO] Axiom selection finished. Selected 532 axioms (removed 0 axioms).
% 5.14/2.08 % [INFO] Problem is first-order (TPTP FOF).
% 5.14/2.10 % [INFO] Type checking passed.
% 5.14/2.10 % [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 ...
% 20.48/5.86 % External prover 'e' found a proof!
% 20.48/5.86 % [INFO] Killing All external provers ...
% 20.48/5.86 % Time passed: 5307ms (effective reasoning time: 4646ms)
% 20.48/5.86 % 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)>
% 20.48/5.86 % Axioms used in derivation (532): fact_add__le__less__mono, fact_xt1_I1_J, fact_le__SucI, fact_Pi__I, fact_insertCI, fact_surj__f__inv__f, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_card__image__le, arity_fun__Orderings_Oorder, fact_folding__image__simple__idem_Osubset__idem, fact_nat_Osimps_I3_J, fact_pos__add__strict, fact_n_I2_J, fact_add__strict__right__mono, fact_Ints__odd__nonzero, fact_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_xt1_I4_J, fact_unanimity__def, fact_trans__less__add1, fact_injD, fact_folding__image__simple__idem_Oin__idem, fact_nat__add__left__commute, fact_order__le__less__trans, fact_image__insert, fact__C1_C, fact_nat__less__cases, fact_Pi__mono, arity_prod__Finite__Set_Ofinite, fact_IIA__def, fact_one__is__add, fact_surjh, fact_funcset__image, fact_termination__basic__simps_I5_J, fact_insert__subset, arity_Nat__Onat__Orderings_Oorder, fact__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_Suc__mono, fact_insertI1, fact_order__less__asym_H, fact__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_image__add__atLeastLessThan, 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, 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_linorder__antisym__conv1, fact_add__nonneg__eq__0__iff, fact_inv__into__image__cancel, fact_equalityD2, fact_card__eq__UNIV__imp__eq__UNIV, fact_add__increasing2, fact_even__less__0__iff, fact_image__Suc__atLeastLessThan, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, 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_finite__nat__set__iff__bounded__le, fact_Pi__mem, fact_inj__on__inv__into, fact_finite__atLeastLessThan, fact_add__0__left, fact_predicate2D, fact_gr0I, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact__096c_A_126_061_Ad_096, arity_HOL__Obool__Orderings_Otop, fact_order__less__imp__not__less, fact_folding__image__simple__idem_Oinsert__idem, fact_less__eq__nat_Osimps_I1_J, fact_lessI, fact_ord__less__eq__trans, fact_in__mono, fact_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_zero__reorient, fact_atLeastLessThan__subset__iff, fact_mkbot__Lin, fact_in__measure, fact_Suc__less__SucD, fact_add__0__right, fact_card__bij, fact_subset__iff__psubset__eq, fact_inj__on__iff__card__le, fact_card__image, fact_nat_Oinject, fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_not__add__less2, fact_less__or__eq__imp__le, fact_funcset__mem, fact_top1I, fact_rev__image__eqI, fact_Suc__leI, fact_add__neg__nonpos, fact_in__finite__psubset, fact_inj__on__contraD, fact_not__less__less__Suc__eq, fact_finite__imageD, fact_card__Plus__conv__if, fact_UNIV__I, fact_le__add2, fact_inj__on__strict__subset, arity_Nat__Onat__Orderings_Opreorder, fact_finite__indi, fact_card__bij__eq, fact_finite__surj, fact_Suc__n__not__le__n, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_Suc__lessD, fact_order__less__imp__not__eq2, fact_order__refl, fact_not__less0, fact_card__psubset, fact_dictator__def, fact_add__left__imp__eq, fact_trans__less__add2, fact_less__Suc__eq__le, fact_card_Oinsert, fact_add__leD2, fact_xt1_I5_J, fact_insert__code, fact_Ints__0, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_inj__on__id2, fact_not__one__less__zero, fact_not__less__eq, fact_zero__le__double__add__iff__zero__le__single__add, fact_nat__neq__iff, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_insert__image, fact_nat_Osimps_I2_J, fact_finite__PlusD_I2_J, fact__C2_C, fact_add__right__cancel, fact_add__less__cancel__left, fact_add__left__cancel, fact_eq__mem, fact_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_insertI2, fact_less__Suc__eq__0__disj, fact_le__Suc__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_insert__absorb, fact_subset__card__intvl__is__intvl, 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, fact_finite__nat__set__iff__bounded, 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_mlex__leq, fact_inv__image__comp, fact_folding__image__simple_Oinsert, fact_nat_Osize_I1_J, fact_range__ex1__eq, 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, 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% 20.48/5.86 % No. of inferences in proof: 1068
% 20.48/5.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5307 ms resp. 4646 ms w/o parsing
% 21.31/6.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.31/6.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------