%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT159+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : 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 08:27:21 AM UTC 2026
% Result : Theorem 29.27s 9.04s
% Output : Refutation 29.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 396
% Syntax : Number of formulae : 794 ( 190 unt; 0 typ; 0 def)
% Number of atoms : 2301 ( 693 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 10593 ( 254 ~; 75 |; 245 &;8832 @)
% ( 101 <=>;1086 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 9 con; 0-6 aty)
% Number of variables : 2272 ( 0 ^;2203 !; 69 ?;2272 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_decl,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_member_decl,type,
c_member: $i > $i > $i > $o ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple__idem_decl,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_decl,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_fTrue_decl,type,
c_fTrue: $i ).
thf(c_fFalse_decl,type,
c_fFalse: $i ).
thf(c_SetInterval_Oord__class_OgreaterThan_decl,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one_decl,type,
c_Finite__Set_Ofolding__one: $i > $i > $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_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Fun_Othe__inv__into_decl,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Groups_Ominus__class_Ominus_decl,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
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_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $i > $o ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Nat_Onat_Onat__size_decl,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_HOL_Obool_Obool__size_decl,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(1322,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
thf(1036,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)],[158]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(1024,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1190,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)],[191]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(1767,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)],[311]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
thf(1995,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)],[377]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(479,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1237,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(909,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(334,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(1850,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)],[334]) ).
thf(187,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1179,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
thf(555,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
thf(1956,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)],[364]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1110,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(1454,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(385,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 ) ) )
=> ( 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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(2031,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 ) ) )
=> ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ? [D: $i,E: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( E @ ( C @ c_Finite__Set_Ocard ) )
= A )
& ~ ( E @ ( D @ ( C @ c_member ) ) )
& ( B
= ( E @ ( D @ ( C @ c_Set_Oinsert ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
thf(1200,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( E @ ( C @ c_Finite__Set_Ocard ) )
= A )
& ~ ( E @ ( D @ ( C @ c_member ) ) )
& ( B
= ( E @ ( D @ ( C @ c_Set_Oinsert ) ) ) ) )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [D: $i,E: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( E
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( E @ ( C @ c_Finite__Set_Ocard ) )
= A )
& ~ ( E @ ( D @ ( C @ c_member ) ) )
& ( B
= ( E @ ( D @ ( C @ c_Set_Oinsert ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( E @ c_Set_Oinsert ) ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert ) ) @ ( B @ ( E @ c_Set_Oinsert ) ) ) )
<=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) )
=> ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( E @ c_Set_Oinsert ) ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert ) ) @ ( B @ ( E @ c_Set_Oinsert ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( E @ c_Set_Oinsert ) ) )
= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( E @ c_Set_Oinsert ) ) @ ( B @ ( E @ c_Set_Oinsert ) ) ) )
=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(683,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(163,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1068,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(256,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(1522,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(1443,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(1618,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(359,axiom,
~ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
thf(1939,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)],[359]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( E @ c_member ) ) )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).
thf(741,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( E @ c_member ) ) )
=> ( ( B
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(1544,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(878,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)],[119]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) )
<=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) ) )
& ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(861,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(1142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(1269,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(1971,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ ( B @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( B @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
thf(1533,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)],[259]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(1705,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(1426,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ~ ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(1671,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(1310,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 ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(550,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(307,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Osize__class_Osize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(1735,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)],[307]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) )
=> ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(1867,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)],[339]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(1260,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)],[200]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(913,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(389,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 ) ) )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(2042,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 ) ) ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member ) ) )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B @ ( D @ ( C @ c_member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
thf(1458,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member ) ) )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B @ ( D @ ( C @ c_member ) ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member ) ) )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B @ ( D @ ( C @ c_member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(829,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( 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 ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(1243,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 ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( 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 ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(78,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(709,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(381,axiom,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
thf(2010,plain,
( ( c_fTrue @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(353,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(1921,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(1386,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 ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( 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)],[227]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(436,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(1518,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(973,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(159,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 ) ) )
<=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(1046,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 ) ) ) )
& ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(243,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(1475,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(2067,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)],[394]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(1529,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(1409,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(838,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(751,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(94,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 ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
thf(802,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 ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(1279,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(460,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(559,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less) ).
thf(638,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1087,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(10,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 ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( D = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
thf(421,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 ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).
thf(1479,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(58,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 ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(606,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 ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
<=> ? [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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(1013,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 ) ) ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ? [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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
thf(1641,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)],[284]) ).
thf(313,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(1773,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(1494,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(342,axiom,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
thf(1875,plain,
( ( c_fFalse @ c_HOL_Obool_Obool__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(1922,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(902,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(120,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(881,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(416,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(221,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(1362,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( 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 ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(367,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_Onat_Onat__size )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
thf(1963,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)],[367]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ~ ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( B @ ( C @ c_Finite__Set_Ocard ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(1664,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(349,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 ) ) )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(1911,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 ) ) )
=> ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1632,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
thf(1418,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(293,axiom,
! [A: $i,B: $i] : ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(1682,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)],[293]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).
thf(514,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) )
& ( ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(182,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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
thf(1151,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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ ( B @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(1960,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)],[366]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
thf(475,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( A @ ( C @ ( B @ c_member ) ) )
<=> ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(924,plain,
! [A: $i,B: $i] :
( ( ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ? [C: $i] : ( A @ ( C @ ( B @ c_member ) ) ) )
& ( ? [C: $i] : ( A @ ( C @ ( B @ c_member ) ) )
=> ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(329,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 ) ) )
<=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(1828,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 ) ) ) )
& ( ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_member ) ) )
=> ? [E: $i] :
( ! [F: $i] :
( ( A
= ( F @ ( B @ hAPP ) ) )
=> ( F = E ) )
& ( A
= ( E @ ( B @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(373,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 ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(1978,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 ) ) )
=> ( ( A @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( 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_OatLeastAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
thf(1183,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( 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_OatLeastAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(205,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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
thf(1283,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(397,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 ) ) ) )
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2073,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 ) ) ) )
=> v_thesis____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member ) ) )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(981,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member ) ) )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) )
=> ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(1843,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)],[331]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(634,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
!= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(866,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(257,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
thf(1526,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(380,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/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
thf(2002,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)],[380]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1600,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(849,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(372,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/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
thf(1975,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)],[372]) ).
thf(42,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
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
thf(546,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
!= ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(1306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(300,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 ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
thf(1708,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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 ) ) ) )
& ( ( 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 ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_Sum__Type_OPlus ) ) ) )
= ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
thf(1783,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)],[317]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(379,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/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
thf(2000,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)],[379]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1730,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member ) ) )
=> ( A @ ( D @ ( B @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member ) ) )
=> ( A @ ( D @ ( B @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(1343,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(176,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(1123,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(266,axiom,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(1570,plain,
tc_HOL_Obool @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).
thf(561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(246,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1487,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(424,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(407,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(429,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert ) ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(1370,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( A
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ c_Groups_Oone__class_Oone )
= A ) )
& ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).
thf(815,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(729,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)],[82]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(1883,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)],[345]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(1423,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)],[233]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(847,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(274,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
thf(1602,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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(369,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(1968,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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(295,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1687,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(281,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(1624,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 ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(165,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(1079,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( 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 ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(178,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 ) ) )
=> ( ( C @ ( A @ ( F @ c_member ) ) )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(1128,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 ) ) )
=> ( ( C @ ( A @ ( F @ c_member ) ) )
=> ( ( B @ ( D @ hAPP ) )
!= ( A @ ( D @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(268,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 ) ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(1573,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 ) ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( 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)],[268]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(852,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ ( D @ c_member ) ) )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member ) ) )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(1555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ ( D @ c_member ) ) )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member ) ) )
=> ( ( ( 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 ) ) )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ c_member ) ) )
=> ( ( ( E @ ( B @ hAPP ) )
= ( F @ ( B @ hAPP ) ) )
=> ( E = F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(948,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless ) ) )
| ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
& ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
thf(783,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oorder )
=> ( ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless ) ) )
| ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
& ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless ) ) )
| ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
& ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(147,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 ) ) )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( D @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
thf(989,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 ) ) )
=> ( ( ( A @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( D @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( D @ ( C @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(1360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(358,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(1936,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member ) ) )
=> ~ ( C @ ( A @ ( B @ c_member ) ) ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member ) ) )
=> ( C @ ( A @ ( B @ c_member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1329,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member ) ) )
=> ~ ( C @ ( A @ ( B @ c_member ) ) ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member ) ) )
=> ( C @ ( A @ ( B @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(933,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(391,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 ) ) )
<=> ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
& ( A
!= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
thf(2053,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 ) ) ) )
& ( ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( 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)],[391]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
thf(2038,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)],[387]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(1644,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(1612,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).
thf(706,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ? [C: $i] : ( A @ ( C @ ( B @ c_member ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
thf(1297,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ? [C: $i] : ( A @ ( C @ ( B @ c_member ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(290,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(1668,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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert ) ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
thf(457,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert ) ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(911,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(1715,plain,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(303,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(1720,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(779,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(1825,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member ) ) )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
thf(1114,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member ) ) ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member ) ) ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member ) ) )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member ) ) )
=> ( ~ ( A @ ( C @ ( D @ c_member ) ) )
=> ( ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(647,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member ) ) )
=> ( ~ ( A @ ( C @ ( D @ c_member ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(314,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1776,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(1099,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(985,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1456,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(1382,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(179,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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
thf(1131,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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less) ).
thf(654,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_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member ) ) ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(1002,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(335,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(1852,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(337,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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
thf(1857,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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(792,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(325,axiom,
! [A: $i] :
( ( tc_HOL_Obool @ ( A @ tc_Option_Ooption @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ tc_Option_Ooption @ c_Finite__Set_Ofinite ) )
<=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
thf(1814,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)],[325]) ).
thf(197,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 ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(1241,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 ) ) )
=> ( A @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_prod ) @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(1779,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)],[315]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(805,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
thf(921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(541,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ v_thesis____,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(398,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member ) ) )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__0__iff) ).
thf(1071,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member ) ) )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member ) ) )
=> ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(674,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(1167,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(376,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(1991,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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member ) ) )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(1318,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member ) ) )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(1712,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(332,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 ) ) )
=> ( ( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(1846,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 ) ) )
=> ( ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(160,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 ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
thf(1054,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 ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( C @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(126,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(906,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(1648,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(365,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(1959,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(386,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 ) ) )
& ( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
thf(2033,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 ) ) )
=> ? [E: $i] :
( ( A @ ( C @ ( E @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( 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 ) ) )
& ( 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 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(573,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
thf(733,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)],[83]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(965,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(305,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 ) ) )
=> ( ( 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 ) ) )
=> ( ( C @ ( F @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( F @ c_Finite__Set_Ocard ) )
= ( B @ ( E @ c_Finite__Set_Ocard ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
thf(1727,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 ) ) )
=> ( ( 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 ) ) )
=> ( ( 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)],[305]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(1510,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(1154,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(819,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(125,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(904,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(74,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(694,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(351,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(1916,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(843,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(826,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
<=> ( ( A @ ( C @ c_Finite__Set_Ofinite ) )
& ( B @ ( D @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
thf(1535,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)],[260]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
thf(1965,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( B @ ( tc_Nat_Onat @ c_Finite__Set_Ocard ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(255,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(1520,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(139,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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(958,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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(1403,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(318,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 ) ) )
<=> ( A @ ( B @ ( E @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(1786,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 ) ) )
=> ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member ) ) ) )
& ( ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_member ) ) )
=> ( A @ ( B @ ( E @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( D @ ( A @ ( B @ c_member ) ) )
<=> ( C @ ( A @ ( B @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( C @ ( A @ ( B @ c_member ) ) )
=> ( D @ ( A @ ( B @ c_member ) ) ) )
& ( ( D @ ( A @ ( B @ c_member ) ) )
=> ( C @ ( A @ ( B @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert ) ) ) )
<=> ( ( B = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
thf(611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
& ( C = B ) )
=> ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert ) ) ) )
=> ( ( B = A )
& ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(168,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 ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( F @ c_member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
thf(1092,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 ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( F @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(167,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(1090,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(283,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(1638,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
thf(713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
thf(498,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(57,axiom,
~ ( c_fFalse @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(604,plain,
~ ( c_fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(831,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(1894,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)],[347]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(419,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(149,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(996,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(1542,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(567,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1144,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(312,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 ) ) )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(1771,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 ) ) )
=> ~ ( A @ ( B @ ( D @ ( C @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
<=> ( ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( B @ c_Finite__Set_Ocard ) )
= ( C @ ( D @ c_Finite__Set_Ocard ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(1801,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)],[321]) ).
thf(296,axiom,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(1690,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(267,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
thf(1571,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)],[267]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(863,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
thf(477,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(343,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 ) ) )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(1877,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 ) ) )
=> ( 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 ) ) ) )
& ( ( 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 ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member ) ) )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(631,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member ) ) )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(552,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(621,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(215,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(1325,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1022,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(1177,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(326,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(1820,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(174,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1112,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(462,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(162,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 ) ) )
=> ( ( C @ ( A @ ( F @ c_member ) ) )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(1061,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 ) ) )
=> ( ( C @ ( A @ ( F @ c_member ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) )
& ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( C @ c_Finite__Set_Ocard ) )
= ( A @ ( D @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
thf(1952,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)],[362]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(868,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member ) ) )
<=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(883,plain,
! [A: $i,B: $i] :
( ( ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member ) ) ) )
& ( ! [C: $i] :
~ ( A @ ( C @ ( B @ c_member ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(608,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(1000,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(244,axiom,
! [A: $i] : ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
thf(1477,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)],[244]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(1102,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(371,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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(1973,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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(192,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 ) ) )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(1198,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 ) ) )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(330,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(1841,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
thf(1926,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)],[355]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1594,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [E: $i] :
( ( E @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( E @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__SucD) ).
thf(1699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ ( D @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ? [E: $i] :
( ( E @ ( C @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( E @ ( D @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(390,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 ) ) )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
thf(2051,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 ) ) )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(695,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(722,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Sum__Type_OPlus ) ) ) @ ( C @ ( D @ tc_sum ) @ c_Finite__Set_Ofinite ) )
=> ( B @ ( D @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
thf(1034,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)],[157]) ).
thf(323,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 ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(1809,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 ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Fun_Oinj__on ) ) ) )
=> ( ( B @ ( A @ ( C @ ( C @ c_Set_Oimage ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(341,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(1873,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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(589,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(663,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(232,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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(1420,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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(294,axiom,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(1684,plain,
! [A: $i,B: $i] :
~ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(812,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(263,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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
thf(1547,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ocard ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(1798,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)],[320]) ).
thf(113,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 ) ) )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
thf(855,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 ) ) )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_sum ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_sum ) @ c_Finite__Set_Ofinite ) )
<=> ( ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) )
& ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
thf(2012,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)],[382]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(1605,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
thf(993,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( 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)],[148]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(1516,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(1598,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(1941,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)],[360]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(1252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
thf(1790,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)],[319]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(1432,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(239,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1452,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(585,plain,
! [A: $i,B: $i,C: $i] :
( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
thf(502,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).
thf(840,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(201,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 ) ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(1262,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 ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(348,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 ) ) )
& ( D @ ( E @ ( B @ ( C @ c_Fun_Oinj__on ) ) ) ) )
<=> ? [E: $i] :
( ( A @ ( E @ ( C @ ( B @ c_Set_Oimage ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
thf(1901,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 ) ) )
& ( 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 ) ) )
& ( 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)],[348]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(1658,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
thf(1218,plain,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member ) ) )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B @ ( D @ ( C @ c_member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
thf(1220,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member ) ) )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B @ ( D @ ( C @ c_member ) ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( B @ ( A @ ( tc_Nat_Onat @ ( C @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ ( E @ ( C @ c_member ) ) )
=> ( ( D != E )
=> ( ( E @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( D @ ( A @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B @ ( D @ ( C @ c_member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(544,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(190,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 ) ) )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(1188,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 ) ) )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
thf(1186,plain,
! [A: $i,B: $i] :
( ( B @ class_Finite__Set_Ofinite )
=> ( A @ ( B @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
thf(1934,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)],[357]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(744,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(374,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(1981,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 ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( C @ ( A @ ( B @ c_member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(1506,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
=> ~ ( C @ ( A @ ( B @ c_member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1749,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 ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( 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)],[309]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
thf(1504,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)],[249]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(1094,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(384,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2030,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(571,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(344,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 ) ) )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(1881,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 ) ) )
=> ( A @ ( C @ ( D @ ( E @ c_Fun_Oinj__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member ) ) )
=> ( B @ ( A @ ( D @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(1353,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(363,axiom,
tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_Finite__Set_Ofinite ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
thf(1955,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)],[363]) ).
thf(39,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 ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(539,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 ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(264,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 ) ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(1553,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 ) ) )
=> ( B @ ( C @ c_Finite__Set_Ofinite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( A @ ( B @ tc_fun ) @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ tc_fun ) @ c_Finite__Set_Ofinite ) )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(1913,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)],[350]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(1126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(1010,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(1289,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(396,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(2071,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(1807,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)],[322]) ).
thf(378,axiom,
( ( tc_Nat_Onat @ c_Orderings_Obot__class_Obot )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
thf(1998,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)],[378]) ).
thf(361,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/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
thf(1949,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)],[361]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(482,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)],[25]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) )
<=> ( ( A @ ( C @ ( D @ c_member ) ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member ) ) )
| ( C = B ) )
=> ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) )
=> ( ( A @ ( C @ ( D @ c_member ) ) )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(581,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(316,axiom,
( ( tc_HOL_Obool @ ( tc_Product__Type_Ounit @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Product__Type_Ounit @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
thf(1781,plain,
( ( tc_HOL_Obool @ ( tc_Product__Type_Ounit @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_Product__Type_Ounit @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member ) ) )
<=> ( A @ ( C @ ( B @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( A @ ( C @ ( B @ c_member ) ) )
=> ( A @ ( D @ ( B @ c_member ) ) ) )
& ( ( A @ ( D @ ( B @ c_member ) ) )
=> ( A @ ( C @ ( B @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
thf(1590,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)],[269]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(1646,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(699,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(963,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(336,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(1854,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
thf(1822,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)],[327]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1491,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( C @ ( D @ c_member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(667,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( C @ ( D @ c_member ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( C @ ( D @ c_member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(1440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(211,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(1308,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(393,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(2066,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
thf(1607,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(252,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(1513,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).
thf(899,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite ) )
=> ( ( B @ ( A @ ( C @ c_member ) ) )
=> ( ( B @ ( C @ c_Finite__Set_Ocard ) )
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(43,axiom,
c_fTrue @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(549,plain,
c_fTrue @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member ) ) )
<=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(716,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member ) ) ) )
& ( ( A @ ( B @ ( C @ c_member ) ) )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(14,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(433,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 ) ) )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(510,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(383,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/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
thf(2019,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)],[383]) ).
thf(61,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(620,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(292,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1678,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(405,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__singleton) ).
thf(1303,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_Nat_Onat @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(105,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
thf(833,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(7,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_OatLeastAtMost ) ) ) )
<=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
thf(410,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) ) )
& ( ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( B @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(950,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)],[136]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( ( A @ class_Finite__Set_Ofinite )
& ( B @ class_Finite__Set_Ofinite ) )
=> ( A @ ( B @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
thf(1097,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)],[170]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( tc_Nat_Onat @ 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_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( 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_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).
thf(835,plain,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) )
= ( tc_Nat_Onat @ 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_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( 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_OatLeastAtMost ) ) @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Big__Operators_Ocomm__monoid__add__class_Osetsum ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(270,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
thf(1593,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(338,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(1859,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(375,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 ) ) )
=> ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(1989,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 ) ) )
=> ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member ) ) )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(506,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member ) ) )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(807,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(1693,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Finite__Set_Ocard ) ) )
=> ( A
= ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(1891,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)],[346]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(960,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(388,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 ) ) )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(2040,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 ) ) )
=> ( B @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(1165,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(138,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 ) ) )
=> ( ( C @ ( A @ ( F @ c_member ) ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(955,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 ) ) )
=> ( ( C @ ( A @ ( F @ c_member ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member ) ) )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member ) ) )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(392,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(2063,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(277,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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(1610,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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(1930,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(84,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(740,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member ) ) )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
thf(987,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member ) ) )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
thf(464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Olinorder )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( ( 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)],[20]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(427,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1357,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(822,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(1004,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) ) )
| ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(691,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) ) )
| ( B
= ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(280,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(1621,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(29,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(501,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(596,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member ) ) ) )
& ( ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(1378,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(486,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(935,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( 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 ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(1737,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(333,axiom,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(1848,plain,
! [A: $i,B: $i] : ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ ( B @ c_member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(1917,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(496,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
=> ( ( A @ ( B @ c_Finite__Set_Ocard ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(1870,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)],[340]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(1449,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(324,axiom,
! [A: $i] :
( ( A @ class_Finite__Set_Ofinite )
=> ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
thf(1812,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)],[324]) ).
thf(5156,plain,
$false,
inference(e,[status(thm)],[1322,1036,809,1024,1190,1767,1995,479,1237,909,1850,1179,555,1295,1956,1110,1454,2031,1200,762,683,1068,1522,1443,1618,1939,741,1544,878,677,861,1142,1269,1971,1533,1705,1426,1671,1310,550,1735,1867,1260,913,2042,1458,829,1243,709,2010,1921,1386,436,1518,973,1046,1724,1475,2067,1529,1409,504,838,751,802,1279,460,559,638,1087,421,1479,606,1013,1641,1773,1494,1875,1922,902,881,416,1362,1963,1415,1664,1911,1632,1418,1682,514,1151,1960,475,924,1828,1978,1183,1283,2073,981,1843,634,866,1526,2002,1600,849,1975,546,1306,1708,1783,534,2000,1730,1057,1343,952,1123,1570,561,1487,424,407,429,1370,815,729,1883,1423,847,1602,1968,1687,1624,583,1079,1128,1573,852,1555,948,403,783,989,1360,1936,1329,933,2053,2038,1644,1612,706,1297,1668,457,911,1715,1720,779,1759,1825,1114,647,1776,1099,985,1456,1382,1131,654,1002,1852,1857,792,1814,1241,1779,805,921,541,398,1071,674,1167,1991,1318,1712,1846,1054,906,1648,1959,2033,573,733,965,1727,1510,1154,819,904,694,1916,843,826,1535,1965,1520,958,1403,1786,1271,611,1092,1090,919,1638,713,498,604,831,1894,419,996,1542,567,1144,1771,1801,1690,1571,863,477,1877,631,552,621,520,1325,1022,1177,1820,1112,462,1061,1952,868,883,608,1000,1477,1102,1973,2069,1198,1841,1926,399,1594,1699,2051,695,473,722,1034,1809,1873,589,663,1420,1684,812,1547,1798,855,2012,1605,993,1516,1598,1941,1252,1790,1432,1452,585,502,840,1262,1901,1658,1218,1220,544,1188,1186,1934,744,1981,1506,1749,1504,1094,2030,571,1881,859,1353,1955,539,1553,1913,759,1126,1010,1289,2071,1807,1998,1949,482,524,581,1781,891,1590,1646,699,963,1854,1822,1491,667,1440,1308,2066,1607,1513,899,549,716,433,510,536,2019,620,447,1678,405,1303,833,410,950,1097,835,1593,1380,1859,1989,506,807,1693,1891,960,2040,1165,955,796,2063,1610,1930,740,987,464,427,1384,1357,822,1004,691,1621,501,596,1378,486,935,1737,1848,1917,496,1870,1449,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT159+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n007.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 06:32:24 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.80/1.15 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.16/1.72 % [INFO] Parsing done (568ms).
% 2.16/1.75 % [INFO] Running in sequential loop mode.
% 3.25/2.30 % [INFO] eprover registered as external prover.
% 3.25/2.30 % [INFO] Scanning for conjecture ...
% 3.63/2.52 % [INFO] Found a conjecture (or negated_conjecture) and 532 axioms. Running axiom selection ...
% 4.40/2.86 % [INFO] Axiom selection finished. Selected 395 axioms (removed 137 axioms).
% 5.92/3.43 % [INFO] Problem is first-order (TPTP FOF).
% 5.92/3.46 % [INFO] Type checking passed.
% 5.92/3.47 % [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 ...
% 28.58/9.03 % External prover 'e' found a proof!
% 29.27/9.03 % [INFO] Killing All external provers ...
% 29.27/9.03 % Time passed: 8384ms (effective reasoning time: 7272ms)
% 29.27/9.03 % 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)>
% 29.27/9.03 % Axioms used in derivation (395): fact_setsum__shift__lb__Suc0__0, fact_xt1_I1_J, fact_le__SucI, fact_singleton__iff, fact_insertCI, fact_pos__add__strict, fact_finite_Oequations_I1_J, 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_atLeastLessThan__empty__iff2, fact_atLeastAtMost__singleton_H, fact_subset__UNIV, fact_finite_OemptyI, fact_nat__add__left__commute, fact_insert__iff, fact_image__insert, fact_greaterThan__subset__iff, fact_card__gt__0__iff, fact_le__eq__less__or__eq, fact_one__is__add, fact_xt1_I4_J, fact_trans__less__add1, fact_injD, fact_folding__image__simple__idem_Oin__idem, fact_nat__less__cases, arity_prod__Finite__Set_Ofinite, fact_termination__basic__simps_I5_J, fact_insert__subset, fact_less__imp__le__nat, arity_Nat__Onat__Orderings_Oorder, fact_Suc__mono, fact_less__nat__zero__code, fact_insertI1, fact_add__leD1, arity_sum__Finite__Set_Ofinite, fact_nat_Osize_I4_J, fact_linorder__not__le, fact_finite, fact_add__less__mono, fact_UNIV__not__empty, fact_nat__add__right__cancel, fact_gr0__conv__Suc, fact_linorder__neqE, fact_inj__on__the__inv__into, fact_leI, fact_the__inv__f__f, fact_empty__not__insert, fact_Suc__le__mono, fact_inj__image__mem__iff, fact_linorder__antisym__conv2, fact_card_Oempty, fact_atLeastLessThanSuc, fact_le__neq__implies__less, fact_finite__code, fact_zero__le__one, fact_finite__Plus__UNIV__iff, fact_nat__add__left__cancel__less, fact_atLeastAtMost__singleton, fact_atLeastatMost__subset__iff, help_c__fFalse__1, fact_setsum__eq__Suc0__iff, fact_linorder__antisym__conv3, fact_order__less__imp__not__eq, fact_insert__not__empty, fact_card__eq__UNIV__imp__eq__UNIV, arity_Option__Ooption__Finite__Set_Ofinite, fact_linorder__antisym__conv1, fact_equalityD2, fact_image__Suc__atLeastLessThan, fact_finite__atLeastLessThan, fact_gr0I, fact_singleton__inject, fact_emptyE, fact_finite__Prod__UNIV, fact_finite__UNIV, fact_folding__one_Oinsert, fact_finite__nat__set__iff__bounded__le, fact_add__0__iff, fact_folding__one__idem_Oin__idem, fact_linorder__less__linear, fact_folding__image__simple__idem_Oinsert__idem, fact_less__eq__nat_Osimps_I1_J, fact_lessI, fact_in__mono, fact_termination__basic__simps_I4_J, fact_le__iff__add, fact_one__reorient, fact_xt1_I9_J, fact_less__add__eq__less, fact_add__lessD1, fact_add__le__mono1, fact_zero__reorient, fact_atLeastLessThan__subset__iff, fact_nat_Oinject, fact_Suc__less__SucD, fact_subset__singletonD, fact_Suc__leI, fact_inj__on__contraD, fact_inj__on__iff__card__le, fact_card__image, fact_not__add__less2, fact_less__or__eq__imp__le, fact_top1I, fact_rev__image__eqI, fact_atLeastLessThan__empty__iff, fact_subset__iff__psubset__eq, fact_not__less__less__Suc__eq, fact_finite__imageD, fact_card__Plus__conv__if, fact_UNIV__I, fact_le__add2, fact_inj__on__strict__subset, fact_card__bij__eq, fact_finite__surj, fact_Suc__n__not__le__n, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_finite__indi, fact_atLeastAtMost__singleton__iff, fact_Suc__lessD, fact_order__less__imp__not__eq2, fact_not__less0, fact_card__psubset, fact_trans__less__add2, fact_less__Suc__eq__le, fact_card_Oinsert, fact_add__leD2, fact_xt1_I5_J, fact_insert__code, fact_not__one__less__zero, fact_not__less__eq, fact_folding__one__idem_Ohom__commute, fact_nat__neq__iff, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_folding__one__idem_Oinsert__idem, fact_insert__image, fact_nat_Osimps_I2_J, fact_finite__PlusD_I2_J, fact_ex__in__conv, fact_finite__UNIV__card__ge__0, fact_nat__size, fact_subset__insertI, 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_bool_Osize_I2_J, fact_finite__insert, fact_insert__absorb2, fact_insertI2, fact_less__Suc__eq__0__disj, fact_folding__one__idem_Oidem, fact_finite__fun__UNIVD1, fact_equals0D, fact_le__Suc__eq, fact_insert__absorb, fact_subset__card__intvl__is__intvl, fact_inj__image__eq__iff, fact_subset__insert, fact_rev__finite__subset, fact_eqset__imp__iff, fact_less__antisym, fact_order__neq__le__trans, fact_not__one__le__zero, fact_Suc__le__eq, fact_equalityD1, fact_finite__option__UNIV, fact_subset__image__iff, fact_inj__on__def, fact_inj__on__iff, fact_finite__nat__set__iff__bounded, fact_less__eq__Suc__le, fact_less__add__Suc2, fact_insert__commute, fact_finite__imageI, fact_linorder__neq__iff, fact_nat_Osize_I1_J, fact_range__ex1__eq, fact_all__not__in__conv, fact_empty__is__image, fact_Plus__eq__empty__conv, fact_set__mp, fact_bool_Osize_I1_J, fact_psubset__card__mono, fact_linorder__neqE__nat, fact_not__less__iff__gr__or__eq, fact_card__ge__0__finite, fact_psubsetD, arity_Nat__Onat__Groups_Ozero, fact_add__is__1, fact_ex__nat__less, fact_inj__image__subset__iff, fact_card__insert__if, fact_order__less__le, fact_card__Plus, fact_not__add__less1, fact_psubset__trans, fact_xt1_I12_J, fact_subset__inj__on, fact_Suc__le__lessD, fact_image__Suc__atLeastAtMost, fact_set__eq__subset, fact_folding__one__idem_Osubset__idem, arity_Product____Type__Ounit__Finite__Set_Ofinite, fact_Suc__inject, fact_equalityI, fact_subset__refl, fact_ext, arity_fun__Finite__Set_Ofinite, fact_atLeastatMost__empty__iff2, fact_card__eq__0__iff, fact_Suc__neq__Zero, fact_empty__iff, fact_card__mono, fact_add__eq__self__zero, arity_HOL__Obool__Orderings_Oorder, fact_linorder__le__less__linear, fact_finite__atLeastAtMost, fact_nat__add__left__cancel, fact_endo__inj__surj, arity_Nat__Onat__Orderings_Olinorder, fact_linorder__le__cases, fact_setsum__eq__1__iff, fact_card__UNIV__unit, fact_n__not__Suc__n, fact_nat__le__linear, fact_all__nat__less, fact_card__inj__on__le, fact_not__leE, fact_leD, fact_insert__ident, fact_add__Suc, fact_add__gr__0, fact_image__is__empty, fact_psubset__imp__subset, fact_singletonE, fact_rangeI, fact_atLeastatMost__psubset__iff, fact_nat_Osize_I2_J, fact_subset__empty, fact_set__rev__mp, fact_card__insert__disjoint, fact_ex__nat__less__eq, fact_eq__mem__trans, fact_inj__on__iff__eq__card, fact_the__inv__into__into, fact_Suc__eq__plus1__left, fact_Zero__not__Suc, fact_pigeonhole, fact_Suc__leD, fact_zero__less__one, fact_setsum__SucD, fact_linorder__linear, fact_less__trans__Suc, fact_xt1_I6_J, fact_subset__insertI2, arity_HOL__Obool__Finite__Set_Ofinite, fact_less__not__refl2, fact_le__add1, fact_trans__le__add2, fact_le__refl, fact_nat__add__assoc, fact_linorder__not__less, fact_add__is__0, fact_termination__basic__simps_I3_J, fact_atLeastLessThan__singleton, fact_le__imp__less__Suc, fact_xt1_I2_J, fact_less__add__Suc1, fact_all__nat__less__eq, fact_rev__predicate1D, fact_One__nat__def, fact_equalityE, fact_Suc__eq__plus1, fact_atLeastAtMostSuc__conv, fact_atLeastLessThan__empty, fact_image__iff, fact_subset__psubset__trans, fact_empty__subsetI, fact_the__inv__into__onto, fact_Zero__neq__Suc, fact_card__seteq, fact_finite__fun__UNIVD2, fact_greaterThan__0, fact_order__eq__iff, arity_Nat__Onat__Rings_Olinordered__semidom, fact_not__less__eq__eq, fact_less__not__refl, fact_insert__mono, fact_card_Oremove, fact_le0, fact_ex__least__nat__less, fact_the__inv__into__f__eq, fact_greaterThan__eq__iff, fact_equalityCE, fact_gr__implies__not0, fact_finite_OinsertI, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_atLeastLessThan__inj_I2_J, fact_f__the__inv__into__f, fact_le__trans, fact_image__eqI, fact_less__add__one, fact_subsetD, fact_less__Suc__eq, fact_nat__add__commute, fact_range__eqI, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_Suc__less__eq, fact_eq__card__imp__inj__on, fact_psubset__eq, fact_add__leE, fact_the__inv__into__f__f, fact_atLeastLessThan0, fact_zero__less__Suc, fact_card_Oneutral, help_c__fTrue__1, fact_plus__nat_Oadd__0, fact_inj__Suc, fact_finite__PlusD_I1_J, fact_le__SucE, fact_eq__imp__le, fact_finite__surj__inj, fact_image__mono, fact_infinite__UNIV__nat, fact_card__Suc__eq, fact_order__le__imp__less__or__eq, fact_nat_Osize_I3_J, fact_insertE, fact_le__less__Suc__eq, fact_inj__onD, fact_Suc__n__not__n, fact_subset__trans, fact_le__antisym, fact_trans__le__add1, fact_eqelem__imp__iff, fact_card__infinite, fact_atLeastLessThan__inj_I1_J, fact_le__0__eq, fact_finite__UNIV__surj__inj, fact_psubset__subset__trans, fact_order__antisym__conv, fact_neq0__conv, fact_finite__subset, fact_finite__UNIV__inj__surj, fact_not__psubset__empty, fact_zero__less__two, conj_0, fact_add__le__mono, fact_less__Suc0, fact_order__le__less, fact_iso__tuple__UNIV__I, fact_termination__basic__simps_I1_J, fact_less__iff__Suc__add, fact_add__imp__eq, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_image__empty, fact_nat__less__le, fact_card__insert__le, fact_less__SucE, fact_atLeastLessThanSuc__atLeastAtMost, fact_finite__Plus, arity_Nat__Onat__Groups_Oone, fact_mem__def, fact_linorder__cases, fact_add__less__mono1, fact_xt1_I11_J, fact_inj__on__empty, fact_ab__semigroup__add__class_Oadd__ac_I1_J, fact_atLeastatMost__empty, fact_add__Suc__shift, fact_doubleton__eq__iff, fact_folding__image__simple__idem_Oidem, fact_xt1_I7_J, fact_inj__on__iff__surj, fact_bot__nat__def, fact_atLeastLessThan__eq__iff, fact_finite__Plus__iff, fact_UNIV__Plus__UNIV, fact_imageI, fact_less__SucI, fact_Suc__not__Zero, fact_Suc__lessI, fact_add__Suc__right, fact_setsum__eq__0__iff, fact_atLeastatMost__empty__iff
% 29.27/9.03 % No. of inferences in proof: 794
% 29.27/9.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8384 ms resp. 7272 ms w/o parsing
% 29.13/9.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.13/9.35 % [INFO] Killing All external provers ...
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