%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT161+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:22 AM UTC 2026
% Result : Theorem 48.38s 13.43s
% Output : Refutation 49.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 535
% Syntax : Number of formulae : 1072 ( 253 unt; 0 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 : 0 ( 0 >; 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_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(v_h_____decl,type,
v_h____: $i ).
thf(v_Sledgehammer_058p__2_decl,type,
v_Sledgehammer_058p__2: $i ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(v_Lba_____decl,type,
v_Lba____: $i ).
thf(v_Lab_____decl,type,
v_Lab____: $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_decl,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(v_F_decl,type,
v_F: $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_b_____decl,type,
v_b____: $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_Oord__class_OgreaterThan_decl,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i > $i ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Fun_Othe__inv__into_decl,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_decl,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(class_Groups_Oordered__comm__monoid__add_decl,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_member_decl,type,
c_member: $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i ).
thf(c_If_decl,type,
c_If: $i > $i ).
thf(c_Arrow__Order__Mirabelle_OProf_decl,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Wellfounded_Olex__prod_decl,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(class_Groups_Ocancel__semigroup__add_decl,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_decl,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_Arrow__Order__Mirabelle_OLin_decl,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_decl,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_FuncSet_OPi_decl,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i ).
thf(class_Groups_Olinordered__ab__group__add_decl,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(c_SetInterval_Oord_OgreaterThan_decl,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_decl,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(c_Big__Operators_Ocomm__monoid__add__class_Osetsum_decl,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i > $i > $i ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(c_Finite__Set_Ofolding__one__idem_decl,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Wellfounded_Omax__extp_decl,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple__idem_decl,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_Wellfounded_Omlex__prod_decl,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Recdef_Osame__fst_decl,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_fTrue_decl,type,
c_fTrue: $i ).
thf(c_Arrow__Order__Mirabelle_Odictator_decl,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_decl,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_fFalse_decl,type,
c_fFalse: $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_decl,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_HOL_Obool_Obool__size_decl,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(c_SetInterval_Oord_OatLeast_decl,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_Wellfounded_Omax__ext_decl,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_decl,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_decl,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_decl,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_Wellfounded_Ofinite__psubset_decl,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Nat_Onat_Onat__size_decl,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(c_Wellfounded_Omeasure_decl,type,
c_Wellfounded_Omeasure: $i > $i > $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(c_SetInterval_Oord_OatLeastAtMost_decl,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_FunDef_Oin__rel_decl,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(2163,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(201,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1337,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij__eq) ).
thf(1024,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( A @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(1190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(65,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(760,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( D @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).
thf(2109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( D @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2072,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(1237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(481,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(2544,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(666,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1950,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2250,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(2595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
thf(2427,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) ) )
<=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__is__image) ).
thf(1083,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) ) )
=> ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(1750,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
thf(582,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(374,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
thf(2104,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(56,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(730,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(411,axiom,
v_Lab____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(2231,plain,
v_Lab____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(2527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).
thf(2248,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).
thf(741,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(2014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(281,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(1728,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
thf(597,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(1041,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1522,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(2644,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(378,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(2114,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(1269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj) ).
thf(1793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(241,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1533,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(162,axiom,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1173,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complete__Lin) ).
thf(1486,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(399,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
thf(2195,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(1655,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(514,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2686,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(1756,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
thf(550,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) ) ) )
& ( ( ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(1867,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(2141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(499,axiom,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
thf(2627,plain,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(93,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(913,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(142,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(1095,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(1001,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
thf(2046,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( D @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( D @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ ( E @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(782,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(709,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(301,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(1803,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(1904,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(235,axiom,
! [A: $i] : ( c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C0_C) ).
thf(1518,plain,
! [A: $i] : ( c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1703,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
thf(1628,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1287,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).
thf(570,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(1430,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2339,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( C @ ( A @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(1826,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(249,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(1577,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(3,axiom,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(542,plain,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(1409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(724,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(510,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
thf(2667,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(719,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(462,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_emptyE) ).
thf(2444,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(189,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1264,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(406,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
thf(2217,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(232,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(1511,plain,
c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( C @ ( D @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( C @ ( D @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(2745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
thf(2691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ ( D @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
thf(559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(1800,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(638,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1609,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(969,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(247,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(1568,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(2520,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
thf(2456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(395,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(2178,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(465,axiom,
~ ( v_Lba____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(2451,plain,
~ ( v_Lba____ @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(1858,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(1151,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ( ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(345,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(1960,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(352,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2017,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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(1383,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(574,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(2254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(2508,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(1447,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(866,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
thf(660,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(1943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(2154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(1696,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(2367,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(414,axiom,
~ ( v_Lab____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(2242,plain,
~ ( v_Lab____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2639,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(373,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(2103,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( F @ ( B @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( F @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C4_C) ).
thf(2750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( ( F @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( D @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(1104,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(1242,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(2011,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(942,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(793,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(2646,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(2232,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(1736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(2061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
thf(2589,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(176,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite ) )
<=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
thf(1223,plain,
! [A: $i] :
( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite ) ) )
& ( ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) )
<=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(2601,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) )
& ( ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(1343,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
thf(1021,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( E @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(1355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(267,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1666,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
thf(2032,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2414,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(2396,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(1274,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(2441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ ( C @ c_COMBK ) @ ( D @ ( C @ ( A @ tc_fun ) @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( C @ ( A @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__fun) ).
thf(2673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ ( C @ c_COMBK ) @ ( D @ ( C @ ( A @ tc_fun ) @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( C @ ( A @ tc_fun ) @ ( D @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(61,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(746,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(1091,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(1570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Otop )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
thf(1174,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Otop )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( C @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(2133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1824,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(387,axiom,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ofinite ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__indi) ).
thf(2150,plain,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ofinite ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
thf(566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Set_Oimage ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(1920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(305,axiom,
~ ! [A: $i] :
( ( A @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1819,plain,
~ ! [A: $i] :
( ( A @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).
thf(1210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(440,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2345,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(533,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2741,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(410,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Nat_Onat_Onat__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
thf(2228,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ c_Nat_Onat_Onat__size @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(1740,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(974,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(1012,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ? [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( D @ ( E @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
<=> ? [E: $i] :
( ( A @ ( E @ ( C @ ( B @ c_Set_Oimage ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
thf(852,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( B @ c_Set_Oimage ) ) ) )
= D )
=> ? [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( D @ ( E @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) ) )
& ( ? [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( D @ ( E @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
=> ? [E: $i] :
( ( A @ ( E @ ( C @ ( B @ c_Set_Oimage ) ) ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2663,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
thf(1888,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ ( c_fFalse @ ( tc_HOL_Obool @ c_Nat_Onat_Onat__case ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(38,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(665,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(1027,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( C @ ( A @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
thf(2327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( C @ ( A @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(2213,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(682,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2211,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(2313,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(2492,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(1259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(1953,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(28,axiom,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Fun_Oinj__on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injh) ).
thf(615,plain,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Fun_Oinj__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(443,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(2359,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(518,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(2694,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(269,axiom,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
thf(1672,plain,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(291,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1755,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(150,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(1118,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(118,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(989,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(697,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
thf(1234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(1541,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(2157,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(2115,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(489,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( B @ c_FuncSet_OPi ) ) ) @ ( B @ c_COMBI @ ( B @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
thf(2577,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( B @ c_FuncSet_OPi ) ) ) @ ( B @ c_COMBI @ ( B @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(1064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) )
& ( ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(980,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1587,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(1878,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(2726,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(1138,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
<=> ( C @ ( D @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
thf(1719,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Omax__extp ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
=> ( C @ ( D @ c_Wellfounded_Omax__ext ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(1683,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
thf(933,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
thf(2561,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1,conjecture,
( ~ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( v_Sledgehammer_058p__2 @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ = v_Lab____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ~ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( v_Sledgehammer_058p__2 @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ = v_Lab____ ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(537,plain,
~ ( ~ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( v_Sledgehammer_058p__2 @ ( v_h____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_Lba____ = v_Lab____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(669,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(1700,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(173,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(1214,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1644,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(1039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(218,axiom,
c_fTrue @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(1419,plain,
c_fTrue @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(2419,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta) ).
thf(1075,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ ( tc_HOL_Obool @ ( D @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(483,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__0) ).
thf(2551,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThan ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(2085,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(6,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(547,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
thf(1744,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(2504,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(2125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(701,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(243,axiom,
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjh) ).
thf(1539,plain,
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(2598,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).
thf(1192,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equals0D) ).
thf(1060,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(911,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(487,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(2566,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(11,axiom,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
thf(569,plain,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
thf(779,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(25,axiom,
! [A: $i] : ( c_Arrow__Order__Mirabelle_OProf @ ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiProf) ).
thf(605,plain,
! [A: $i] : ( c_Arrow__Order__Mirabelle_OProf @ ( v_Lba____ @ ( v_Lab____ @ ( A @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( F @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij) ).
thf(1525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( B @ ( F @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( F @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( F @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(158,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1150,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(1249,plain,
! [A: $i,B: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ? [E: $i] :
( ( A @ ( C @ ( E @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) )
<=> ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
thf(2536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( C @ ( E @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) )
& ( ? [E: $i] :
( ( A @ ( C @ ( E @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ ( E @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) )
=> ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(1297,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
thf(1831,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(1231,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(2697,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(1246,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(316,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).
thf(1857,plain,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(402,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(2203,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2546,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(2043,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(921,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(2057,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(1732,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(674,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(460,axiom,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(2440,plain,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
thf(1515,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(408,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2221,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
thf(953,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(508,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).
thf(2662,plain,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(906,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(1906,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(111,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
thf(965,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1747,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(733,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(1135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(2729,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(1648,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(2524,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(2376,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(584,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) )
& ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
thf(694,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(1916,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( D @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
thf(1884,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( D @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(1620,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1752,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(743,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(826,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(1795,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(1520,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
thf(545,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( E @ ( D @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).
thf(936,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( E @ ( D @ ( C @ c_COMBB ) ) ) @ hAPP ) @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( G @ ( B @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( E @ ( E @ c_Set_Oimage ) ) ) @ ( C @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( B @ hAPP ) )
= ( G @ ( B @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( A
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( B @ ( E @ ( E @ c_Set_Oimage ) ) ) @ ( C @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(1312,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
thf(2738,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(1865,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( B @ ( D @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
thf(572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( B @ ( D @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(2029,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(435,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(2326,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(1239,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Obot )
=> ( ( A @ ( C @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( C @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(1997,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(393,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(2166,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(294,axiom,
tc_HOL_Obool @ class_Orderings_Otop,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(1765,plain,
tc_HOL_Obool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(1464,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(947,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Otop )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
<=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
thf(1194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Wellfounded_Omax__extp ) ) ) )
=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( A
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( A @ ( D @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__empty) ).
thf(2151,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2383,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(1894,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(784,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(1806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ c_Wellfounded_Ofinite__psubset @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(2669,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(649,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(616,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1376,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(2065,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(416,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(2246,plain,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1492,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(1603,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
thf(2299,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(2182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(2025,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
thf(609,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(2267,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(621,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(81,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(848,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(110,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(964,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(1112,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(2180,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( B @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
thf(758,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( B @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(202,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(1339,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(381,axiom,
tc_HOL_Obool @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(2129,plain,
tc_HOL_Obool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(2343,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(75,axiom,
~ ( v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
thf(799,plain,
~ ( v_Lba____ @ ( v_Lab____ @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( v_h____ @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_If @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( v_F @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(726,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(2593,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(1029,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
thf(2278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) )
=> ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) )
& ( C @ ( D @ c_Finite__Set_Ofinite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(2553,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(1177,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(2075,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(1926,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(1594,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(959,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
thf(883,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( A @ ( B @ ( C @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta_H) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( E @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( c_fequal @ hAPP ) @ ( E @ c_If @ ( D @ ( E @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( E @ tc_fun ) @ ( E @ ( D @ c_COMBS ) ) ) ) @ ( E @ ( E @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( B @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(372,axiom,
~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
thf(2101,plain,
~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
thf(2390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( B
!= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ! [E: $i] :
( ( C @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( F @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( D @ c_Wellfounded_Omax__ext ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
thf(1841,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oord )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(1396,plain,
! [A: $i,B: $i] :
( ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ? [C: $i] : ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1528,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).
thf(868,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(1583,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(224,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(1467,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(34,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(648,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(939,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(1958,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(491,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite ) )
<=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
thf(2582,plain,
! [A: $i,B: $i] :
( ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite ) ) )
& ( ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(1304,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
thf(1873,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
thf(795,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(2318,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(423,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2271,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(37,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(663,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(2652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(2449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(1509,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(1081,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
thf(749,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
thf(2629,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(437,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL )
<=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(2333,plain,
! [A: $i,B: $i] :
( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(2256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(2564,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(165,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1181,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(823,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ocard ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(1845,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ocard ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
thf(580,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
thf(1961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(137,axiom,
~ ! [A: $i] :
( ( A @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1070,plain,
~ ! [A: $i] :
( ( A @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
thf(707,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(2732,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(2518,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(1368,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1267,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(2720,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B != A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(1098,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( B != A )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).
thf(557,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(1003,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(2143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(1484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(2160,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
thf(993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL )
=> ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(516,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
thf(2689,plain,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__is__empty) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( A
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(2224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(717,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(407,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2219,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
thf(576,plain,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__empty) ).
thf(2701,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( B @ ( C @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(285,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(1738,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(1220,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
<=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(2656,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(2747,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ c_Arrow__Order__Mirabelle_Ounanimity )
<=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(1499,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ c_Arrow__Order__Mirabelle_Ounanimity ) )
& ( ( A @ c_Arrow__Order__Mirabelle_Ounanimity )
=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(1188,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(167,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1186,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(309,axiom,
v_Lba____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(1830,plain,
v_Lba____ @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(1763,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(1130,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(1579,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(513,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
thf(2675,plain,
! [A: $i,B: $i] :
( ( ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(1257,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(1141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Fun_Oinj__on ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) )
& ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(2379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(2711,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(2579,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1670,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(527,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(2722,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).
thf(1881,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(2411,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(469,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
thf(2500,plain,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(1543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ c_Arrow__Order__Mirabelle_OIIA )
<=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1766,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) )
=> ( A @ c_Arrow__Order__Mirabelle_OIIA ) )
& ( ( A @ c_Arrow__Order__Mirabelle_OIIA )
=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(2357,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(23,axiom,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(600,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(253,axiom,
( c_Arrow__Order__Mirabelle_OProf
= ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_FuncSet_OPi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Prof__def) ).
thf(1585,plain,
( c_Arrow__Order__Mirabelle_OProf
= ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_FuncSet_OPi ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
thf(978,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(529,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2728,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
thf(595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( A @ ( C @ ( D @ c_Fun_Othe__inv__into ) ) ) @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(991,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(1617,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1940,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(1918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(671,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Set_Oimage ) ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(1157,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(2215,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(2611,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(1216,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(429,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(2305,plain,
! [A: $i,B: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(502,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(2643,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(1734,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(1108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(226,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(1476,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(632,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(1244,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(2130,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(731,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(2416,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
thf(961,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(813,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1341,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
thf(896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ c_FuncSet_OPi ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ? [E: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B @ ( E @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(1674,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(1639,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(103,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096F_A_I_Fi_O_ALba_J_A_058_ALin_096) ).
thf(946,plain,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(1101,plain,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( D @ c_Finite__Set_Ocard ) @ ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(2447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( D @ c_Finite__Set_Ocard ) @ ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(2009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(2648,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(195,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(1294,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( A @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
thf(1440,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( A @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(763,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(371,axiom,
~ ! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Set_Oimage ) ) ) )
!= ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(2095,plain,
~ ! [A: $i] :
( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( tc_Nat_Onat @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Set_Oimage ) ) ) )
!= ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(426,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(2294,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).
thf(2315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ocard ) )
= ( A @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(2421,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(1133,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(1348,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(999,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(1512,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1725,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(343,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(1957,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(143,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(1097,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(1229,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(475,axiom,
( ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__nat__def) ).
thf(2522,plain,
( ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(1876,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(197,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(1303,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( E @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( D @ ( B @ ( E @ c_COMBB ) ) ) @ hAPP ) @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( E @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( D @ ( B @ ( E @ c_COMBB ) ) ) @ hAPP ) @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(790,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(603,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(149,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(1116,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(1908,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(263,axiom,
~ ( c_fFalse @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1642,plain,
~ ( c_fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(752,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ ( B @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C3_C) ).
thf(833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( E @ ( B @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1314,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(304,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(1816,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(2186,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2704,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(767,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(524,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(2714,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(2619,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(107,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(955,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcsetI) ).
thf(886,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) @ hAPP ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(2201,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(801,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1693,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__empty) ).
thf(2070,plain,
! [A: $i,B: $i,C: $i] : ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(1346,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(1930,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).
thf(2502,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Obot )
=> ( A @ ( B @ c_Orderings_Obot__class_Obot @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(188,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oempty) ).
thf(1261,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(240,axiom,
tc_Nat_Onat @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(1532,plain,
tc_Nat_Onat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
thf(1537,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1713,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_sum ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_sum ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( C @ ( D @ tc_sum ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( A
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
& ( B
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(251,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(1582,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(2265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(1597,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(2687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1902,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(691,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(2321,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(923,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(1184,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).
thf(543,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(676,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(466,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(2453,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(1812,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(2087,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(1848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(361,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(2059,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(1037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite ) )
=> ( A @ ( D @ c_Finite__Set_Ocard ) @ ( B @ ( E @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(427,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(2297,plain,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(2438,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(2238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
thf(2170,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
thf(2351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
thf(592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(225,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(1468,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(1870,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(972,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(3172,plain,
$false,
inference(e,[status(thm)],[2163,1337,1024,1190,760,2109,2072,1237,2544,666,1950,2250,2595,1850,2427,1083,1750,582,1005,2104,730,2231,2527,2248,741,2014,1728,597,1041,1522,2644,2114,1269,1793,1533,1173,1486,2195,1655,2686,1756,550,1867,2141,2627,913,1095,1001,2046,2432,782,709,2067,1803,1904,1518,1703,1628,1287,570,1430,2339,2708,619,1826,1577,542,1409,724,2667,719,2444,1264,2217,1511,2274,917,949,2745,2691,559,1800,638,1609,969,1568,2520,2456,2178,2027,2451,1858,1828,1151,1677,1960,2017,1383,574,2254,2508,1447,866,1394,660,1943,2154,2718,1696,2367,1928,2242,2639,2103,2750,1405,1104,1242,2011,942,678,793,2646,2232,1736,2061,2589,1223,2601,1343,1021,2541,1355,862,2147,1666,2032,2414,2396,1274,2441,2673,746,1091,1570,1174,2133,1824,2150,566,1920,1819,1159,1210,2345,2741,2228,2112,1740,974,1012,852,2663,1888,665,1027,2327,2213,682,2211,2313,2492,578,1259,1953,615,2359,2694,1672,1755,1118,989,697,1234,1541,2157,2115,2577,1064,980,1587,1878,2726,1138,1719,1683,2323,933,2561,537,669,1700,1791,1214,1644,1039,1419,2419,1075,2551,2085,547,1744,2504,2125,701,1539,2598,1192,1060,911,2566,569,779,605,1525,1150,1249,2536,1297,1831,1231,2697,1246,1857,2203,2546,2043,921,2057,773,1732,926,674,2440,1515,2221,953,2662,906,1906,965,1747,733,1135,2729,1648,2524,2376,584,1833,694,1916,1884,1620,1752,743,826,1795,1520,545,936,1271,1312,2738,1865,1058,572,2029,2326,1239,1997,2166,1765,1464,947,1194,2151,2383,1894,784,1806,1933,2669,649,616,1376,2197,2065,2246,1492,1603,2299,2182,2025,609,2267,621,848,964,1112,890,2180,758,1339,2129,2343,799,726,2593,1029,2278,2553,1177,1381,2075,1926,1594,959,883,1015,2244,2101,2390,1841,1396,1528,868,2005,1583,2107,1467,1420,648,939,1958,2582,1304,1873,795,2318,2271,663,2652,2449,1509,1081,749,2629,2333,2256,2564,1181,823,1845,1798,580,1961,1070,707,2732,2518,1368,1267,2720,1098,557,1003,1566,2143,1484,2160,993,2689,2569,2224,717,2219,576,2701,1738,1220,2656,2747,1499,1188,1186,1830,1763,1130,1579,2675,1257,1141,2379,2711,2579,1670,2722,1881,2411,2500,1543,1766,2357,600,1585,978,2728,1717,1372,595,991,1617,1940,2435,1918,671,1157,1412,2215,2611,1216,2305,2643,1734,1108,1476,632,1244,2130,731,2416,961,813,1341,896,1674,1639,946,1101,2447,2009,914,2041,2648,1294,1440,763,2095,2294,2315,2421,1133,1348,999,1512,1725,1957,2534,1097,1229,2522,1876,1303,1148,790,603,1116,1908,1642,752,833,967,1314,1816,2186,2704,767,2714,2619,955,886,2201,801,1693,2070,1346,2063,1930,2502,1261,2430,1532,1537,908,1713,1120,607,1582,2265,1597,2687,1902,691,2321,923,1184,543,676,2453,1812,2087,1848,2059,1037,2297,2438,2238,2170,2351,592,1468,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT161+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.49 % Computer : n007.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 06:32:40 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.45/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.42/1.97 % [INFO] Parsing done (635ms).
% 3.42/1.99 % [INFO] Running in sequential loop mode.
% 4.86/2.56 % [INFO] eprover registered as external prover.
% 4.86/2.57 % [INFO] Scanning for conjecture ...
% 5.67/2.87 % [INFO] Found a conjecture (or negated_conjecture) and 534 axioms. Running axiom selection ...
% 7.54/3.20 % [INFO] Axiom selection finished. Selected 534 axioms (removed 0 axioms).
% 10.00/4.00 % [INFO] Problem is first-order (TPTP FOF).
% 10.65/4.06 % [INFO] Type checking passed.
% 10.65/4.07 % [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 ...
% 48.38/13.42 % External prover 'e' found a proof!
% 48.38/13.42 % [INFO] Killing All external provers ...
% 48.38/13.42 % Time passed: 12732ms (effective reasoning time: 11425ms)
% 48.38/13.43 % 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)>
% 48.38/13.43 % 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, 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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
% 48.38/13.43 % No. of inferences in proof: 1072
% 48.38/13.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12732 ms resp. 11425 ms w/o parsing
% 49.89/13.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.89/13.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------