TSTP Solution File: SCT161+1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SCT161+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 : Tue May 7 08:05:32 EDT 2024
% Result : Theorem 126.80s 34.81s
% Output : Refutation 127.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 633
% Syntax : Number of formulae : 1170 ( 253 unt; 98 typ; 0 def)
% Number of atoms : 3214 ( 800 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 24285 ( 347 ~; 68 |; 321 &;21796 @)
% ( 142 <=>;1611 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 177 ( 177 >; 0 *; 0 +; 0 <<)
% Number of symbols : 100 ( 98 usr; 18 con; 0-6 aty)
% Number of variables : 3207 ( 0 ^3149 !; 58 ?;3207 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(v_h_____type,type,
v_h____: $i ).
thf(v_Sledgehammer_058p__2_type,type,
v_Sledgehammer_058p__2: $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(v_Lba_____type,type,
v_Lba____: $i ).
thf(v_Lab_____type,type,
v_Lab____: $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_type,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(v_F_type,type,
v_F: $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(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_b_____type,type,
v_b____: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_Oord__class_OgreaterThan_type,type,
c_SetInterval_Oord__class_OgreaterThan: $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_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_type,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $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(c_member_type,type,
c_member: $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i ).
thf(c_If_type,type,
c_If: $i > $i ).
thf(c_Arrow__Order__Mirabelle_OProf_type,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
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_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(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
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_FuncSet_OPi_type,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $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(c_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(c_Big__Operators_Ocomm__monoid__add__class_Osetsum_type,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i > $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_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Wellfounded_Omax__extp_type,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $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(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $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_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_fTrue_type,type,
c_fTrue: $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_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_fFalse_type,type,
c_fFalse: $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_HOL_Obool_Obool__size_type,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(c_SetInterval_Oord_OatLeast_type,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_Wellfounded_Omax__ext_type,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
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(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_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(2452,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(1024,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)],[135]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(1190,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)],[182]) ).
thf(262,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1559,plain,
~ ( hBOOL @ c_fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1729,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)],[305]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(893,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)],[97]) ).
thf(536,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/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).
thf(2595,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)],[536]) ).
thf(519,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/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(2544,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)],[519]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(666,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)],[43]) ).
thf(456,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/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
thf(2295,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)],[456]) ).
thf(461,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/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(2306,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)],[461]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(760,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)],[69]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1454,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)],[238]) ).
thf(385,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/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(2031,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)],[385]) ).
thf(484,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/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
thf(2412,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)],[484]) ).
thf(194,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(1237,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(488,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(2427,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(1083,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)],[151]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(777,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)],[75]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
thf(555,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)],[8]) ).
thf(363,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/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(1956,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)],[363]) ).
thf(360,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/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
thf(1950,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)],[360]) ).
thf(451,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/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(2280,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)],[451]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1110,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)],[160]) ).
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/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(1924,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(225,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/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(1406,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)],[225]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(683,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)],[47]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
thf(730,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)],[61]) ).
thf(478,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/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2395,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)],[478]) ).
thf(330,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/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(1808,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)],[330]) ).
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/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(2590,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(380,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/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(2014,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)],[380]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(873,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)],[89]) ).
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/sandbox/benchmark/theBenchmark.p',fact_leI) ).
thf(2099,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(411,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/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(2114,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)],[411]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(1437,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)],[231]) ).
thf(469,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
thf(2363,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(343,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(1855,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
thf(1158,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)],[171]) ).
thf(462,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(2309,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(762,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)],[70]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(878,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(2380,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)],[473]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(614,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)],[30]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(677,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)],[45]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(1426,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)],[229]) ).
thf(286,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_Fun_Othe__inv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
thf(1655,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_Fun_Othe__inv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(1137,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)],[167]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1310,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)],[208]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2035,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)],[386]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(1735,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)],[307]) ).
thf(499,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(2476,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)],[499]) ).
thf(389,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/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(2042,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)],[389]) ).
thf(217,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(1354,plain,
hBOOL @ c_fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(109,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(930,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(240,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1458,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(2575,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(376,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/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
thf(1999,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)],[376]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(797,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)],[77]) ).
thf(465,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/sandbox/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(2316,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)],[465]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(715,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)],[57]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
thf(2448,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( class_Orderings_Otop @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(913,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Otop @ B )
=> ( class_Orderings_Otop @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(1063,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)],[146]) ).
thf(362,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/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1954,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)],[362]) ).
thf(439,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2216,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
thf(2227,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)],[442]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(709,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)],[54]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(1613,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)],[274]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(1935,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)],[357]) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(1645,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)],[282]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(651,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)],[36]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(1127,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)],[163]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__empty) ).
thf(2548,plain,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_OPi @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(2067,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(257,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1529,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)],[257]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(724,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)],[59]) ).
thf(299,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/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(1709,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)],[299]) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
thf(1792,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)],[326]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oimage @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oimage @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(350,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(1907,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)],[350]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(1826,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)],[335]) ).
thf(201,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(1279,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)],[201]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(2185,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2126,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)],[415]) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
thf(1462,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)],[241]) ).
thf(468,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/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(2356,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)],[468]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
thf(542,plain,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
thf(853,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)],[85]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(1379,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)],[221]) ).
thf(273,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/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(1609,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)],[273]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(969,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)],[123]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(770,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)],[72]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(1494,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
thf(1963,plain,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
thf(1778,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Set_Oimage @ E @ D @ C @ B ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(514,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2533,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
thf(1100,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)],[156]) ).
thf(354,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/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(1922,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)],[354]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
thf(902,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)],[99]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(1319,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)],[210]) ).
thf(297,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/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(1704,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)],[297]) ).
thf(223,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(1398,plain,
class_Orderings_Opreorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(881,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)],[93]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ? [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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
thf(1415,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ? [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
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/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2105,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(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
thf(591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
thf(1373,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)],[220]) ).
thf(345,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(1858,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1828,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)],[336]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(1020,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(266,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1581,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(1051,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)],[141]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(905,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)],[100]) ).
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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(2178,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(441,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/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2222,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)],[441]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( c_Set_Oimage @ C @ D @ B @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
thf(1040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( c_Set_Oimage @ C @ D @ B @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( c_Set_Oimage @ C @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(498,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/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(2469,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)],[498]) ).
thf(365,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/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(1960,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)],[365]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',fact__C3_C) ).
thf(806,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)],[79]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(1183,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)],[179]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(1283,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)],[203]) ).
thf(398,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/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(2073,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)],[398]) ).
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/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(2058,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(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(687,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)],[48]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
thf(692,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)],[49]) ).
thf(472,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/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(2371,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)],[472]) ).
thf(420,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/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(2137,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)],[420]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(1345,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)],[215]) ).
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/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2103,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(436,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(2205,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(533,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2586,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(471,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/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(2367,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)],[471]) ).
thf(490,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/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
thf(2437,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)],[490]) ).
thf(500,axiom,
( ( c_HOL_Obool_Obool__size @ c_fTrue )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
thf(2483,plain,
( ( c_HOL_Obool_Obool__size @ c_fTrue )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(956,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)],[118]) ).
thf(513,axiom,
! [A: $i,B: $i] :
( ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
thf(2523,plain,
! [A: $i,B: $i] :
( ( ( ( c_Finite__Set_Ocard @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ) )
& ( ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( 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)],[513]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(1072,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)],[149]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',fact_funcset__image) ).
thf(2002,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)],[377]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(998,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)],[130]) ).
thf(285,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/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(1651,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)],[285]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Sum__Type_OPlus @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_sum @ D @ C ) @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Sum__Type_OPlus @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_sum @ D @ C ) @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( c_Sum__Type_OPlus @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_sum @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(187,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
thf(1206,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(6,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(546,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(925,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)],[107]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(1306,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)],[207]) ).
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/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(1783,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(443,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/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(2232,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)],[443]) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(2083,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)],[400]) ).
thf(474,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/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(2382,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)],[474]) ).
thf(279,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/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1636,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)],[279]) ).
thf(529,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2574,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(1438,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)],[232]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(1047,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)],[140]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(1057,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)],[144]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(1163,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)],[173]) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(1723,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)],[303]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(1091,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)],[154]) ).
thf(524,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(2560,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(2249,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)],[446]) ).
thf(518,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/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(2541,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)],[518]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(1519,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)],[255]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(1355,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)],[218]) ).
thf(199,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 ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1255,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 ) ) @ ( 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 ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(161,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1123,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1676,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)],[294]) ).
thf(422,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/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(2147,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)],[422]) ).
thf(290,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1666,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(788,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)],[76]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
thf(2132,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)],[418]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(1502,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)],[249]) ).
thf(80,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(820,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(11,axiom,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
thf(566,plain,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(353,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/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1920,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)],[353]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(1968,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)],[368]) ).
thf(239,axiom,
class_Orderings_Obot @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(1457,plain,
class_Orderings_Obot @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
thf(1819,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)],[333]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(2200,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)],[434]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
thf(757,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1281,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)],[202]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(1195,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(2211,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(310,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/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(1740,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)],[310]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(1910,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)],[351]) ).
thf(504,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/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(2498,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)],[504]) ).
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/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2515,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(328,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1804,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)],[328]) ).
thf(344,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/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(1856,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)],[344]) ).
thf(268,axiom,
( ( c_HOL_Obool_Obool__size @ c_fFalse )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
thf(1587,plain,
( ( c_HOL_Obool_Obool__size @ c_fFalse )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(508,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/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(2509,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)],[508]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
thf(593,plain,
! [A: $i,B: $i] :
( ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(989,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)],[128]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(2300,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)],[458]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
<=> ( ( c_Finite__Set_Ofinite @ D @ B )
& ( c_Finite__Set_Ofinite @ D @ A )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
thf(1143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
=> ( ( c_Finite__Set_Ofinite @ D @ B )
& ( c_Finite__Set_Ofinite @ D @ A )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) )
& ( ( ( c_Finite__Set_Ofinite @ D @ B )
& ( c_Finite__Set_Ofinite @ D @ A )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(412,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/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(2115,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)],[412]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(1851,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)],[342]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(1772,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)],[319]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',fact_injh) ).
thf(610,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)],[28]) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(1755,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)],[314]) ).
thf(497,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/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(2460,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)],[497]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(884,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)],[94]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(933,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)],[111]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(669,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)],[44]) ).
thf(463,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/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(2312,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)],[463]) ).
thf(340,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/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(1842,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)],[340]) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(1810,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)],[331]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(1214,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)],[190]) ).
thf(521,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/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2551,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)],[521]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(1739,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)],[309]) ).
thf(1,conjecture,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ v_Sledgehammer_058p__2 ) ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) )
=> ( v_Lba____ = v_Lab____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ v_Sledgehammer_058p__2 ) ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) )
=> ( v_Lba____ = v_Lab____ ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(537,plain,
~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ v_h____ @ v_Sledgehammer_058p__2 ) ) @ ( c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool ) ) ) ) )
=> ( v_Lba____ = v_Lab____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(1700,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)],[295]) ).
thf(358,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/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(1937,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)],[358]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(2108,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)],[409]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
thf(2038,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)],[387]) ).
thf(235,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 ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(1446,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 ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',fact_leD) ).
thf(837,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)],[83]) ).
thf(453,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/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(2285,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)],[453]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(701,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)],[51]) ).
thf(516,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(2536,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)],[516]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(1539,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)],[259]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(654,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)],[38]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(1192,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)],[183]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(1060,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)],[145]) ).
thf(507,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(2505,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)],[507]) ).
thf(503,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(2497,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(526,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/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(2566,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)],[526]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(1002,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)],[132]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
thf(569,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)],[13]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(1246,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)],[197]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(1715,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(1720,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)],[302]) ).
thf(370,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/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(1979,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)],[370]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B @ A ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
thf(605,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fact_card__bij) ).
thf(1451,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)],[237]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
thf(738,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)],[63]) ).
thf(424,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/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2153,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)],[424]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1231,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)],[193]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(1333,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(372,axiom,
~ ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
thf(1991,plain,
~ ( c_Finite__Set_Ofinite @ tc_Nat_Onat @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(1202,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)],[185]) ).
thf(106,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(921,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(3,axiom,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(541,plain,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(657,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)],[39]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
thf(1170,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)],[175]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(1286,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)],[204]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(1466,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)],[243]) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1663,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)],[289]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(1167,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)],[174]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1616,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)],[275]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(1086,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)],[152]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(938,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)],[113]) ).
thf(300,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/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(1712,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)],[300]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(1054,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)],[143]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(662,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)],[41]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(888,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)],[95]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1135,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)],[166]) ).
thf(317,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/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(1764,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)],[317]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(1103,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)],[158]) ).
thf(423,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/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(2149,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)],[423]) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
thf(1927,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)],[356]) ).
thf(86,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 ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcsetI) ).
thf(856,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 ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
thf(573,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)],[15]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_PiProf) ).
thf(601,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)],[25]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(965,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)],[121]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1510,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)],[253]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(1219,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)],[192]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ C @ B @ E @ D ) ) @ A ) ) )
<=> ? [E: $i] :
( ( c_Set_Oimage @ B @ C @ E @ A )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
thf(824,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ C @ B @ E @ D ) ) @ A ) ) )
=> ? [E: $i] :
( ( c_Set_Oimage @ B @ C @ E @ A )
= D ) )
& ( ? [E: $i] :
( ( c_Set_Oimage @ B @ C @ E @ A )
= D )
=> ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Set_Oimage @ C @ B @ E @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
thf(1631,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)],[278]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(733,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)],[62]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(975,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)],[124]) ).
thf(338,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/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
thf(1833,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)],[338]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(694,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)],[50]) ).
thf(391,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/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(2048,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)],[391]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ B ) ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
thf(772,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ B ) ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ 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 @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ B ) ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(1752,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)],[313]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(743,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)],[65]) ).
thf(18,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ A )
=> ( class_Finite__Set_Ofinite @ ( tc_Option_Ooption @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
thf(579,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite @ A )
=> ( class_Finite__Set_Ofinite @ ( tc_Option_Ooption @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
thf(958,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(1965,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)],[367]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
thf(1124,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)],[162]) ).
thf(419,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/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2134,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)],[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/sandbox/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).
thf(2514,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(527,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(2568,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)],[527]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(875,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)],[90]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
thf(577,plain,
! [A: $i,B: $i] :
( ( class_Finite__Set_Ofinite @ B )
=> ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(641,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)],[35]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(1139,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)],[168]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
thf(1786,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(2220,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)],[440]) ).
thf(384,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/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(2029,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)],[384]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1707,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)],[298]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(611,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(713,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)],[56]) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1733,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)],[306]) ).
thf(375,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(1997,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)],[375]) ).
thf(492,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/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
thf(2442,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)],[492]) ).
thf(487,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/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(2425,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)],[487]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',fact_surjh) ).
thf(1464,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)],[242]) ).
thf(293,axiom,
class_Orderings_Otop @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(1675,plain,
class_Orderings_Otop @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(2457,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(105,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 @ E ) @ B ) @ ( c_Set_Oimage @ F @ E @ D @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
thf(919,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 @ E ) @ B ) @ ( c_Set_Oimage @ F @ E @ D @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(523,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/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(2557,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)],[523]) ).
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/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
thf(2521,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(188,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1209,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ D @ tc_Nat_Onat @ C ) @ c_Nat_OSuc ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ D @ tc_Nat_Onat @ C ) @ c_Nat_OSuc ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(486,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/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
thf(2422,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)],[486]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(1806,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)],[329]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(1524,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)],[256]) ).
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/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(2097,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(269,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/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(1589,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)],[269]) ).
thf(246,axiom,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(1492,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(12,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
thf(567,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(92,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(880,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(616,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)],[31]) ).
thf(433,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2197,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)],[433]) ).
thf(485,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/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(2415,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)],[485]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(1894,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)],[347]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(1571,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)],[265]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(599,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)],[24]) ).
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/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(2065,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(176,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(1175,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)],[176]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(631,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)],[33]) ).
thf(464,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/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(2314,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)],[464]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
thf(2111,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)],[410]) ).
thf(373,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(1993,plain,
class_Orderings_Oorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(483,axiom,
( ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
thf(2410,plain,
( ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1029,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)],[136]) ).
thf(261,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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(1556,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)],[261]) ).
thf(447,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/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(2252,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)],[447]) ).
thf(177,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_Oabove @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(1177,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_Oabove @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(361,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/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(1952,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)],[361]) ).
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/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(2578,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(96,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(890,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)],[96]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(1667,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
thf(2180,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ D @ B )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ 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 ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
thf(2261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ D @ B )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ 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 ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(1821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(626,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)],[32]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(915,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)],[104]) ).
thf(102,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ v_F @ ( 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 ) @ v_Lba____ ) ) ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096F_A_I_Fi_O_ALba_J_A_058_ALin_096) ).
thf(912,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ v_F @ ( 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 ) @ v_Lba____ ) ) ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D @ C ) ) ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C @ B ) ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
thf(983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D @ C ) ) ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C @ B ) ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(491,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/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(2439,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)],[491]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
thf(2365,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(480,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/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(2401,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)],[480]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(1066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(401,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/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(2086,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)],[401]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(1643,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)],[281]) ).
thf(421,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/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
thf(2139,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)],[421]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( c_Set_Oimage @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
thf(563,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( c_Set_Oimage @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( c_Set_Oimage @ D @ C @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(383,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/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(2022,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)],[383]) ).
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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
thf(2101,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(459,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/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(2303,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)],[459]) ).
thf(157,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1102,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(425,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/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(2156,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)],[425]) ).
thf(37,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(653,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(397,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(2069,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)],[397]) ).
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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(2051,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(196,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(1245,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(127,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/sandbox/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)],[127]) ).
thf(454,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/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(2288,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)],[454]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(1000,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)],[131]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(1435,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)],[230]) ).
thf(320,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(1775,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)],[320]) ).
thf(535,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/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(2592,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)],[535]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ D @ ( c_SetInterval_Oord__class_OatLeastLessThan @ 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 ) @ A ) @ B ) ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ E @ tc_Nat_Onat @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
thf(1726,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ D @ ( c_SetInterval_Oord__class_OatLeastLessThan @ 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 ) @ A ) @ B ) ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ E @ tc_Nat_Onat @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(1364,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)],[219]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
thf(944,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)],[115]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
thf(927,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
= ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(435,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_Fun_Othe__inv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
thf(2202,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_Fun_Othe__inv__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)],[435]) ).
thf(364,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 ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(1958,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 ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(379,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/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(2005,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)],[379]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(1413,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)],[226]) ).
thf(393,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(2054,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(58,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/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
thf(722,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)],[58]) ).
thf(466,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/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(2318,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)],[466]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(680,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)],[46]) ).
thf(349,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/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
thf(1905,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)],[349]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1420,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)],[228]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1277,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)],[200]) ).
thf(414,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/sandbox/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(2124,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)],[414]) ).
thf(444,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/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(2234,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)],[444]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
thf(1018,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)],[133]) ).
thf(525,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/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(2564,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)],[525]) ).
thf(457,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/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(2298,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)],[457]) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(1516,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)],[254]) ).
thf(34,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(640,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(479,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
thf(2397,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)],[479]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(1070,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)],[148]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(707,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)],[53]) ).
thf(431,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/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(2192,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)],[431]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(1647,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)],[283]) ).
thf(117,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(954,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
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/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(2518,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(427,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/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(2175,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)],[427]) ).
thf(476,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/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(2386,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)],[476]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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 ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) )
<=> ( ( c_Finite__Set_Ofinite @ D @ C )
& ( c_Finite__Set_Ofinite @ D @ B )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
thf(2160,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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 ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) )
=> ( ( c_Finite__Set_Ofinite @ D @ C )
& ( c_Finite__Set_Ofinite @ D @ B )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) ) )
& ( ( ( c_Finite__Set_Ofinite @ D @ C )
& ( c_Finite__Set_Ofinite @ D @ B )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ 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 ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(55,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(712,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
thf(557,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)],[9]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(1770,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(142,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(1053,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(495,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2454,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)],[495]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/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)],[181]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(1038,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)],[138]) ).
thf(416,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(2128,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',fact_injD) ).
thf(1901,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)],[348]) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1658,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)],[287]) ).
thf(164,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1130,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
thf(544,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)],[5]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(1830,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)],[337]) ).
thf(316,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/sandbox/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).
thf(1763,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)],[316]) ).
thf(505,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/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(2500,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)],[505]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(703,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)],[52]) ).
thf(296,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/sandbox/benchmark/theBenchmark.p',fact_card__inj) ).
thf(1702,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)],[296]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(1506,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)],[251]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) )
<=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
thf(864,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
thf(1749,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ 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 @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(60,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(727,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(1797,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)],[327]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(571,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)],[14]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(2266,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)],[450]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(859,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)],[87]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
thf(1141,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)],[169]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(1536,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)],[258]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1585,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)],[267]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(1094,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)],[155]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta_H) ).
thf(978,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(1240,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)],[195]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(991,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)],[129]) ).
thf(359,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/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
thf(1940,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)],[359]) ).
thf(339,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1839,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)],[339]) ).
thf(284,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/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(1649,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)],[284]) ).
thf(402,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/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(2088,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)],[402]) ).
thf(390,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/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(2045,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)],[390]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
thf(1180,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( c_Finite__Set_Ofinite @ E @ B )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
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/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
thf(931,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(332,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/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(1817,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)],[332]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1448,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)],[236]) ).
thf(460,axiom,
class_Finite__Set_Ofinite @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(2305,plain,
class_Finite__Set_Ofinite @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
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/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(1108,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(211,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/sandbox/benchmark/theBenchmark.p',fact__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096) ).
thf(1321,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)],[211]) ).
thf(352,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/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(1913,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)],[352]) ).
thf(432,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/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
thf(2194,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)],[432]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(581,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)],[19]) ).
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/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(1781,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(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ D @ F ) @ G ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ B @ F ) ) @ ( hAPP @ B @ G ) ) )
=> ( ( c_Finite__Set_Ofinite @ E @ A )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ ( c_Set_Oimage @ E @ E @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
thf(1216,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ D @ F ) @ G ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ B @ F ) ) @ ( hAPP @ B @ G ) ) )
=> ( ( c_Finite__Set_Ofinite @ E @ A )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ ( c_Set_Oimage @ E @ E @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(963,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)],[120]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(1341,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)],[214]) ).
thf(280,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(1639,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(455,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/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(2290,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)],[455]) ).
thf(482,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/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2406,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)],[482]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ A @ C ) ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
thf(2554,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ A @ C ) ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',fact_Prof__def) ).
thf(1508,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)],[252]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(946,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(417,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/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
thf(2130,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)],[417]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
thf(588,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)],[20]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(1253,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)],[198]) ).
thf(452,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/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2283,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)],[452]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(2389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(1629,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)],[277]) ).
thf(378,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(2004,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(399,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
thf(2081,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(475,axiom,
( ( c_Orderings_Obot__class_Obot @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
thf(2384,plain,
( ( c_Orderings_Obot__class_Obot @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(1294,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)],[206]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1212,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)],[189]) ).
thf(413,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(2120,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)],[413]) ).
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/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2095,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(374,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
thf(1994,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(2019,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)],[382]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
thf(899,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)],[98]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(1661,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)],[288]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( c_SetInterval_Oord__class_OgreaterThan @ C @ B )
= ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
thf(549,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( ( c_SetInterval_Oord__class_OgreaterThan @ C @ B )
= ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_SetInterval_Oord__class_OgreaterThan @ C @ B )
= ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(502,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/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2494,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)],[502]) ).
thf(234,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 ) ) @ ( 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____ ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C0_C) ).
thf(1444,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 ) ) @ ( 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____ ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(1161,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)],[172]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(800,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)],[78]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(1133,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)],[165]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(1348,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)],[216]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(752,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)],[67]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
thf(1546,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)],[260]) ).
thf(371,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/sandbox/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(1986,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)],[371]) ).
thf(292,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/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(1673,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)],[292]) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(1757,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)],[315]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(603,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)],[26]) ).
thf(515,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/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(2534,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)],[515]) ).
thf(448,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/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2255,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)],[448]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(833,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)],[82]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(967,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)],[122]) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(1395,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)],[222]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1625,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(346,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_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/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
thf(1859,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_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 ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1314,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)],[209]) ).
thf(528,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/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(2572,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)],[528]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1561,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)],[263]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(767,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)],[71]) ).
thf(481,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/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(2404,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)],[481]) ).
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 ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(1742,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)],[311]) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
thf(1789,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)],[325]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(664,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)],[42]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( c_Finite__Set_Ofinite @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(1288,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)],[205]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
thf(839,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)],[84]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(740,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)],[64]) ).
thf(369,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/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(1977,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)],[369]) ).
thf(501,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 ) ) )
<=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( c_Finite__Set_Ofinite @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
thf(2485,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 ) ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( c_Finite__Set_Ofinite @ B @ A ) ) )
& ( ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( c_Finite__Set_Ofinite @ B @ A ) )
=> ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(23,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(596,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)],[23]) ).
thf(532,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/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
thf(2583,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)],[532]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(908,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(1500,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)],[248]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(1597,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)],[271]) ).
thf(506,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/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(2502,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)],[506]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(2241,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Set_Oimage @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Set_Oimage @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Set_Oimage @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(575,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)],[16]) ).
thf(250,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(1505,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(1399,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)],[224]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(935,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(381,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(2018,plain,
class_Orderings_Obot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1848,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)],[341]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(1088,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)],[153]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(1204,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)],[186]) ).
thf(244,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 ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(1468,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 ) ) @ ( 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 ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(1331,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)],[212]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1606,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)],[272]) ).
thf(467,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/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
thf(2321,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)],[467]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(940,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)],[114]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ C ) ) ) @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
thf(2206,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B @ C ) ) ) @ ( hAPP @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(1737,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)],[308]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(659,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)],[40]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(1565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(1490,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)],[245]) ).
thf(74,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____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
thf(775,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____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(12569,plain,
$false,
inference(e,[status(thm)],[2452,1024,1190,1559,1729,893,2595,2544,666,2295,2306,760,1454,2031,2412,1237,2427,1083,777,555,1956,1950,2280,1110,1924,1406,683,730,2395,1808,2590,2014,873,2099,2114,1437,2363,1855,1158,2309,762,878,2380,614,677,1426,1655,1137,1310,2035,1735,2476,2042,1354,930,1458,2575,1999,797,2316,715,2448,747,913,1063,1954,2216,2227,1441,709,1613,1935,1645,651,1127,2548,2067,1529,724,1709,1792,2039,1907,1826,1279,2185,2126,1462,2356,542,853,1379,1609,969,770,1494,1963,1778,2533,1100,1922,902,1319,1704,1398,881,1415,2105,591,1373,1858,1828,1020,1581,1051,905,2178,2222,1040,2469,1960,806,1183,1283,2073,2058,687,692,2371,2137,1345,2103,2205,2586,2367,2437,2483,956,2523,1072,2002,998,1651,1074,1206,546,925,1306,1783,2232,2083,2382,1636,2574,1438,1047,1057,1163,1723,1091,2560,2249,2541,1519,1355,1255,1123,1676,2147,1666,788,2132,1502,820,566,1920,1968,1457,1819,2200,757,1281,1195,2211,1740,1910,2498,2515,1804,1856,1587,2509,593,989,1592,2300,1143,2115,1851,1772,610,1755,2460,884,933,669,2312,1842,1810,1214,2551,1739,537,1700,1937,2108,2038,1446,837,2285,701,2536,1539,654,1192,1060,2505,2497,2566,1002,569,1246,1715,1720,1979,605,1451,738,2153,1231,1333,1991,1202,921,541,657,1170,1286,1466,1663,1167,1616,1185,1086,938,1712,1054,662,888,1135,1764,1103,2149,1927,856,573,601,965,1510,1219,824,1631,733,975,1833,694,2048,772,1752,743,579,958,1965,1124,2134,2514,2568,875,577,641,1139,1786,2220,2029,1707,611,713,1733,1997,2442,2425,1464,1675,2457,919,2557,2521,1209,2538,2422,1806,1524,2097,1589,1492,567,880,616,2197,2415,1894,1571,599,2065,1175,631,2314,2111,1993,2410,1029,1556,2252,1177,1952,2578,890,1667,2180,2261,1821,626,915,912,983,2439,2365,2401,1066,2086,1643,2139,563,2022,2101,2303,1102,2156,653,2069,2051,1245,986,2288,1000,1435,1775,2592,1726,1364,944,927,2202,1958,2005,1413,2054,722,2318,680,1905,1420,1277,2124,2234,1018,2564,2298,1516,640,2397,1070,707,2192,1647,954,2518,2175,2386,2160,712,557,1770,1053,2454,1188,1038,2128,1901,1658,1130,544,1830,1763,2500,703,1702,1506,864,1749,727,1797,571,2266,859,1141,1536,1585,1094,978,1240,991,1940,1839,1649,2088,2045,1180,931,1817,1448,2305,1108,1321,1913,2194,581,1781,1216,963,1341,1639,2290,2406,2554,1508,946,2130,588,1253,2283,2389,1629,2004,2081,2384,1294,1212,2120,2095,1994,2019,899,1661,549,2494,1444,1161,800,1133,1348,752,1546,1986,1673,1757,603,2534,2255,833,967,1395,1625,1859,1314,2572,1561,767,2404,1742,1789,664,1033,1288,839,740,1977,2485,596,2583,908,1500,1597,2502,2241,2430,575,1505,1399,935,2018,1848,1088,1204,1468,1331,1606,2321,940,2206,1737,659,1565,1490,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SCT161+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13 % Command : run_Leo-III %s %d
% 0.13/0.32 % Computer : n032.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 6 11:41:54 EDT 2024
% 0.13/0.32 % CPUTime :
% 0.71/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/0.95 % [INFO] Parsing done (231ms).
% 1.48/0.96 % [INFO] Running in sequential loop mode.
% 2.08/1.21 % [INFO] eprover registered as external prover.
% 2.08/1.21 % [INFO] cvc4 registered as external prover.
% 2.08/1.22 % [INFO] Scanning for conjecture ...
% 2.67/1.36 % [INFO] Found a conjecture and 534 axioms. Running axiom selection ...
% 3.16/1.51 % [INFO] Axiom selection finished. Selected 534 axioms (removed 0 axioms).
% 4.37/1.86 % [INFO] Problem is first-order (TPTP FOF).
% 4.37/1.88 % [INFO] Type checking passed.
% 4.37/1.89 % [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 ...
% 126.80/34.79 % External prover 'e' found a proof!
% 126.80/34.80 % [INFO] Killing All external provers ...
% 126.80/34.81 % Time passed: 34382ms (effective reasoning time: 33839ms)
% 126.80/34.81 % 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)>
% 126.80/34.81 % Axioms used in derivation (534): fact_add__le__less__mono, fact_xt1_I1_J, fact_le__SucI, fact_Pi__I, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_pos__add__strict, fact_add__strict__right__mono, fact_setsum__shift__lb__Suc0__0__upt, fact_finite_Oequations_I1_J, fact_atLeastLessThan__empty__iff2, 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_less__eq__nat_Osimps_I2_J, fact_subset__UNIV, fact_finite_OemptyI, fact__C1_C, fact_greaterThan__subset__iff, fact_card__gt__0__iff, fact_le__eq__less__or__eq, fact_xt1_I4_J, fact_termination__basic__simps_I5_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_nat__less__cases, fact_Pi__mono, arity_prod__Finite__Set_Ofinite, fact_IIA__def, fact_one__is__add, fact_surjh, fact_funcset__image, arity_Nat__Onat__Orderings_Oorder, fact__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_greaterThan__iff, fact_Suc__mono, 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_bot__apply, 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_UNIV__not__empty, fact_order__eq__refl, fact_in__mktop, fact_add__right__imp__eq, fact_image__add__atLeastLessThan, fact_card_Oempty, fact_finite__range__imageI, fact_linorder__neqE, fact_inj__on__the__inv__into, fact_leI, fact_the__inv__f__f, 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, help_c__fequal__2, fact_le__neq__implies__less, fact_add__pos__nonneg, fact_finite__code, 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_bot__fun__def, fact_complete__Lin, fact_add__le__imp__le__left, arity_Option__Ooption__Finite__Set_Ofinite, fact_linorder__antisym__conv1, fact_add__nonneg__eq__0__iff, 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_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_bot__empty__eq, fact_le__funD, fact_add__right__mono, fact_finite__Prod__UNIV, fact_finite__UNIV, fact_finite__nat__set__iff__bounded__le, fact_Pi__mem, fact_finite__atLeastLessThan, fact_add__0__left, fact_predicate2D, fact_gr0I, fact_add__0__iff, fact_folding__one__idem_Oin__idem, fact_emptyE, fact_le__fun__def, fact_le__iff__add, arity_HOL__Obool__Orderings_Otop, fact_less__eq__nat_Osimps_I1_J, fact_lessI, fact_ord__less__eq__trans, fact_in__mono, fact_termination__basic__simps_I4_J, 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_setsum__head__upt__Suc, fact_order__less__imp__not__less, fact_add__lessD1, fact_add__le__mono1, fact_zero__reorient, fact_atLeastLessThan__subset__iff, fact_in__measure, fact_Suc__less__SucD, fact_add__0__right, fact_card__bij, fact_ord_OatMost__iff, fact_inj__on__iff__card__le, fact_card__image, fact_nat_Oinject, fact_max__ext_Osimps, fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096, fact_mkbot__Lin, 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_atLeastLessThan__empty__iff, fact_subset__iff__psubset__eq, 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_ord_OgreaterThan__iff, fact_inj__on__strict__subset, arity_Nat__Onat__Orderings_Opreorder, fact_finite__indi, fact_finite__surj, fact_Suc__n__not__le__n, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_setsum__delta_H, fact_card__bij__eq, fact_Suc__lessD, fact_order__less__imp__not__eq2, fact_order__refl, fact_not__less0, fact_card__psubset, fact_add__left__imp__eq, fact_trans__less__add2, fact_less__Suc__eq__le, fact_xt1_I5_J, fact_add__leD2, fact_max__ext_Ointros, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_setsum__add__nat__ivl, fact_dictator__def, fact_inj__on__id2, fact_not__less__eq, fact_folding__one__idem_Ohom__commute, fact_bot__least, fact_nat_Osimps_I2_J, fact_zero__le__double__add__iff__zero__le__single__add, fact_nat__neq__iff, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_finite__PlusD_I2_J, fact__C2_C, fact_add__right__cancel, fact_add__less__cancel__left, fact_add__left__cancel, fact_ex__in__conv, fact_eq__mem, fact_finite__UNIV__card__ge__0, fact_nat__size, 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, fact_Pi__empty, arity_HOL__Obool__Orderings_Oord, fact_bool_Osize_I2_J, fact__096a_A_126_061_Ab_096, fact_less__Suc__eq__0__disj, fact_folding__one__idem_Oidem, fact_subset__card__intvl__is__intvl, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_inj__image__eq__iff, fact_equals0D, fact_le__Suc__eq, fact_finite__fun__UNIVD1, fact_add__strict__mono, 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_Suc__le__eq, fact_range__composition, fact_equalityD1, fact_finite__option__UNIV, fact_subset__image__iff, fact_max__extp_Oequations, 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__by__empty, fact_less__add__Suc2, fact_in__below, help_c__fequal__1, fact_in__above, fact_finite__imageI, fact_ord__le__eq__trans, fact_linorder__neq__iff, fact_nat_Osize_I1_J, fact_range__ex1__eq, fact_all__not__in__conv, fact_empty__is__image, fact_mlex__leq, fact_Plus__eq__empty__conv, fact_bool_Osize_I1_J, fact_psubset__card__mono, fact_not__less__iff__gr__or__eq, fact_card__ge__0__finite, fact_inj__image__subset__iff, arity_Nat__Onat__Groups_Ozero, fact_add__is__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_set__mp, fact_injh, fact_linorder__neqE__nat, fact_mktop__Lin, fact__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_psubsetD, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, fact_order__less__le, fact__096Lab_A_058_ALin_096, fact_card__Plus, fact_add__nonneg__pos, fact_add__nonpos__nonpos, fact_psubset__trans, fact_xt1_I12_J, fact_setsum__op__ivl__Suc, fact_add__less__cancel__right, fact_ord_OlessThan__iff, fact_subset__inj__on, fact_Suc__le__lessD, arity_Nat__Onat__Orderings_Obot, fact_set__eq__subset, fact_add__increasing, fact_not__add__less1, fact_pred__subset__eq, fact_folding__one__idem_Osubset__idem, fact_Suc__inject, fact_subset__refl, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_fun__Finite__Set_Ofinite, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_zero__less__double__add__iff__zero__less__single__add, fact_card__eq__0__iff, fact_Suc__neq__Zero, fact__C0_C, fact_card__mono, fact_add__eq__self__zero, arity_fun__Orderings_Oord, fact_equalityI, fact_ext, fact_order__less__not__sym, arity_HOL__Obool__Orderings_Oorder, fact_linorder__le__less__linear, arity_fun__Orderings_Obot, fact_empty__iff, fact_nat__add__left__cancel, fact_endo__inj__surj, fact_Prof__def, fact_less__le__not__le, arity_Nat__Onat__Orderings_Olinorder, fact_PiE, fact_linorder__le__cases, fact_assms_I3_J, fact_Pi__UNIV, fact_order__less__le__trans, fact_n__not__Suc__n, fact_nat__le__linear, fact_setsum__shift__bounds__Suc__ivl, help_c__COMBB__1, fact_card__inj__on__le, fact_rangeI, fact_add__Suc, fact_order__less__asym, fact_add__gr__0, arity_fun__Orderings_Otop, fact_image__is__empty, fact_not__leE, fact__096F_A_I_Fi_O_ALba_J_A_058_ALin_096, fact_Pi__eq__empty, fact_leD, fact_add__strict__left__mono, fact_mlex__less, fact_psubset__imp__subset, fact_nat_Osize_I2_J, fact_subset__empty, fact_funcset__id, fact_set__rev__mp, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, fact_ord_OgreaterThanLessThan__iff, fact_eq__mem__trans, fact_inj__on__iff__eq__card, fact_the__inv__into__into, fact_ord_OatLeastLessThan__iff, fact_Zero__not__Suc, fact_pigeonhole, fact_Suc__leD, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_add_Ocomm__neutral, fact_add__less__imp__less__right, fact_ex__nat__less__eq, fact_rev__predicate2D, fact_linorder__linear, fact_less__eq__Suc__le__raw, fact_less__trans__Suc, fact_xt1_I6_J, arity_HOL__Obool__Finite__Set_Ofinite, fact_less__not__refl2, fact_inj__fun, fact_le__add1, fact_trans__le__add2, fact_le__refl, fact_nat__add__assoc, fact_bot2E, fact_linorder__not__less, fact_add__neg__neg, fact_nat__case__Suc, fact_termination__basic__simps_I3_J, fact_add__less__imp__less__left, fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_le__imp__less__Suc, fact_xt1_I2_J, fact_less__add__Suc1, fact_all__nat__less__eq, fact_less__fun__def, 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, fact_rev__predicate1D, fact_in__lex__prod, fact_add__is__0, fact_add__0, fact_equalityE, fact_add__nonneg__nonneg, fact_in__rel__def, fact_atLeastLessThan__empty, fact_subset__psubset__trans, fact_empty__subsetI, fact_the__inv__into__onto, fact_card__inj, fact_Zero__neq__Suc, fact_add__pos__pos, fact_nat__case__0, fact_image__iff, fact_Lin__irrefl, fact_card__seteq, fact_finite__fun__UNIVD2, fact_greaterThan__0, fact_order__eq__iff, fact_bot__empty__eq2, fact_not__less__eq__eq, fact_ord__eq__less__trans, fact_ord_OgreaterThanAtMost__iff, fact_le0, fact_the__inv__into__f__eq, fact_greaterThan__eq__iff, fact_equalityCE, fact_gr__implies__not0, help_c__COMBK__1, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_atLeastLessThan__inj_I2_J, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, fact_add__left__mono, fact_pairwise__neutrality, fact_double__add__le__zero__iff__single__add__le__zero, fact_less__not__refl, fact_f__the__inv__into__f, fact_le__trans, fact_add__less__le__mono, fact_image__eqI, fact_inj__on__add__nat, fact_less__Suc__eq, fact_nat__add__commute, fact_above__Lin, fact_funcsetI, fact_range__eqI, fact_u, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_subsetD, fact_top__greatest, fact_Suc__less__eq, fact_eq__card__imp__inj__on, fact_psubset__eq, fact_add__leE, fact_image__ident, fact_the__inv__into__f__f, fact_atLeastLessThan0, fact_zero__less__Suc, help_c__fTrue__1, fact_plus__nat_Oadd__0, fact_order__le__imp__less__or__eq, fact_inj__Suc, fact_add__nonpos__neg, fact_finite__PlusD_I1_J, fact_le__SucE, fact_setsum__shift__bounds__nat__ivl, fact_dictatorI, fact_eq__imp__le, fact_finite__surj__inj, fact_image__mono, fact_infinite__UNIV__nat, fact_nat_Osize_I3_J, fact_add__strict__increasing, fact_le__less__Suc__eq, fact_inj__onD, fact_setsum__delta, fact_Suc__n__not__n, fact_subset__trans, fact_le__antisym, fact_trans__le__add1, fact_eqelem__imp__iff, fact_atLeastLessThan__inj_I1_J, fact_finite__UNIV__surj__inj, fact_psubset__subset__trans, fact_order__antisym__conv, fact_neq0__conv, fact_card__infinite, fact_ord_OatLeastAtMost__iff, arity_HOL__Obool__Orderings_Obot, fact_pred__equals__eq, fact_double__eq__0__iff, fact_le__0__eq, fact_finite__UNIV__inj__surj, fact_not__psubset__empty, fact__C3_C, fact_add__le__imp__le__right, fact_order__less__irrefl, fact_add__le__mono, fact_less__Suc0, fact_order__le__less, fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_iso__tuple__UNIV__I, fact_less__iff__Suc__add, fact_order__less__imp__le, fact_termination__basic__simps_I1_J, fact_finite__subset, fact_order__less__trans, fact_mem__def, fact_add__imp__eq, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_image__empty, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_nat__less__le, fact_pred__subset__eq2, fact_less__SucE, fact_ord__eq__le__trans, fact_finite__Plus, fact_double__add__less__zero__iff__single__add__less__zero, fact_linorder__cases, fact_xt1_I11_J, fact_add__less__mono1, fact_add__le__cancel__left, fact_inj__on__empty, fact_ab__semigroup__add__class_Oadd__ac_I1_J, fact_add__Suc__shift, fact_folding__image__simple__idem_Oidem, fact_xt1_I7_J, fact_order__trans, fact_inj__on__iff__surj, fact_bot__nat__def, fact_atLeastLessThan__eq__iff, fact_finite__Plus__iff, fact_imageI, fact_less__SucI, fact_Suc__not__Zero, fact_Suc__lessI, fact_add__Suc__right, fact_ord_OatLeast__iff, fact_max__extp__max__ext__eq, fact_const__Lin__Prof, fact_UNIV__Plus__UNIV
% 126.80/34.81 % No. of inferences in proof: 1072
% 126.80/34.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 34382 ms resp. 33839 ms w/o parsing
% 127.72/35.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 127.72/35.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------