%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT042-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:27:05 AM UTC 2026
% Result : Unsatisfiable 22.46s 17.10s
% Output : Refutation 24.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 513
% Syntax : Number of formulae : 1027 ( 413 unt; 0 typ; 0 def)
% Number of atoms : 2019 ( 936 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 11212 ( 880 ~; 992 |; 0 &;9340 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 9 con; 0-5 aty)
% Number of variables : 2738 ( 0 ^;2738 !; 0 ?;2738 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_b_____decl,type,
v_b____: $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Orderings_Oord__class_Omin_decl,type,
c_Orderings_Oord__class_Omin: $i > $i > $i > $i ).
thf(class_Int_Onumber_decl,type,
class_Int_Onumber: $i > $o ).
thf(c_Int_Onumber__class_Onumber__of_decl,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_List_Otake_decl,type,
c_List_Otake: $i > $i > $i > $i ).
thf(c_List_Otl_decl,type,
c_List_Otl: $i > $i > $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Odrop_decl,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_List_Olinorder__class_Osorted_decl,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_List_Olist__update_decl,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Osplice_decl,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_OremoveAll_decl,type,
c_List_OremoveAll: $i > $i > $i > $i ).
thf(c_List_Oremove1_decl,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(c_List_Ohd_decl,type,
c_List_Ohd: $i > $i > $i ).
thf(c_List_Osko__List__XCons__eq__append__conv__1__1_decl,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xappend__eq__Cons__conv__1__1_decl,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xneq__Nil__conv__1__1_decl,type,
c_List_Osko__List__Xneq__Nil__conv__1__1: $i > $i > $i ).
thf(c_List_Osko__List__Xneq__Nil__conv__1__2_decl,type,
c_List_Osko__List__Xneq__Nil__conv__1__2: $i > $i > $i ).
thf(c_List_Onull_decl,type,
c_List_Onull: $i > $i > $o ).
thf(v_sko__CHAINED__1_decl,type,
v_sko__CHAINED__1: $i > $i > $i ).
thf(c_List_Osko__List__Xlist__Xexhaust__1__1_decl,type,
c_List_Osko__List__Xlist__Xexhaust__1__1: $i > $i > $i ).
thf(c_List_Osko__List__Xlist__Xexhaust__1__2_decl,type,
c_List_Osko__List__Xlist__Xexhaust__1__2: $i > $i > $i ).
thf(c_List_Omember_decl,type,
c_List_Omember: $i > $i > $i > $o ).
thf(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1_decl,type,
v_sko__Arrow__Order__Mirabelle__Xthird__alt__1: $i > $i > $i ).
thf(c_List_Olist__inter_decl,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xalt3__1_decl,type,
v_sko__Arrow__Order__Mirabelle__Xalt3__1: $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xalt3__2_decl,type,
v_sko__Arrow__Order__Mirabelle__Xalt3__2: $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xalt3__3_decl,type,
v_sko__Arrow__Order__Mirabelle__Xalt3__3: $i ).
thf(c_List_Osko__List__Xlist__Xnchotomy__1__1_decl,type,
c_List_Osko__List__Xlist__Xnchotomy__1__1: $i > $i > $i ).
thf(c_List_Osko__List__Xlist__Xnchotomy__1__2_decl,type,
c_List_Osko__List__Xlist__Xnchotomy__1__2: $i > $i > $i ).
thf(350,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(227,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1036,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__drop__take_0) ).
thf(1190,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(479,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(1559,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(1295,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(425,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(1501,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(128,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(809,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(1337,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(513,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1718,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(346,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1315,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(1083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(195,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(962,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
thf(1554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(1200,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osize_I4_J_0) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(277,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1158,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__replicate_0) ).
thf(1005,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__0_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(1522,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(1443,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(994,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(453,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1569,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1205,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1591,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(437,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(1533,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OremoveAll ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Osimps_I1_J_0) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OremoveAll ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(284,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(1173,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(730,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__drop_0) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(655,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(229,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1041,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(153,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(861,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Ohd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(1705,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Ohd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(1426,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(1671,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(344,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(1310,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__append_0) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(670,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1507,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(306,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1222,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(1386,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(414,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(1475,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(1254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(138,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(829,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).
thf(1095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(507,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(1703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(339,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1298,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(838,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(802,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__hd__drop_0) ).
thf(1577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(949,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1264,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(917,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
thf(702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(105,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(751,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(131,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(817,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(19,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(559,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(853,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(1247,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(112,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(770,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
thf(881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
thf(1115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(483,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).
thf(1641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(1319,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(870,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1479,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1609,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(924,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(119,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(789,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(1450,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(591,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
= ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(1373,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
= ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_HOL_Oord )
| ~ ( A @ class_Int_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__number__of_1) ).
thf(646,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_HOL_Oord )
| ~ ( A @ class_Int_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(514,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(197,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(966,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1183,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( ( C @ ( B @ ( A @ c_List_Oremove1 ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1__removeAll_0) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( ( C @ ( B @ ( A @ c_List_Oremove1 ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(499,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Ohd ) )
= ( B @ ( A @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(1682,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Ohd ) )
= ( B @ ( A @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
thf(1136,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(375,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(1383,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1020,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(1377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( C @ ( E @ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append_1) ).
thf(1215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( C @ ( E @ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(734,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(1072,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) )
= ( C @ ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) @ ( C @ ( B @ c_List_Ohd ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc_0) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) )
= ( C @ ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) @ ( C @ ( B @ c_List_Ohd ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Omember ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Omember ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(467,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1600,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(450,axiom,
tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__3 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__2 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__1 @ c_List_Olist_OCons ) ) @ c_List_Odistinct ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_alt3_0) ).
thf(1564,plain,
tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__3 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__2 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__1 @ c_List_Olist_OCons ) ) @ c_List_Odistinct ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(956,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1242,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(147,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(849,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(1651,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(186,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(942,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(1306,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1708,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(240,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(1067,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__append_0) ).
thf(714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1636,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( D @ ( B @ ( A @ c_List_OremoveAll ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll__append_0) ).
thf(1163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( D @ ( B @ ( A @ c_List_OremoveAll ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(469,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(1604,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(358,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(1343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
thf(1042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(37,axiom,
tc_nat @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(598,plain,
tc_nat @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(815,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(313,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(1238,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(363,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(1355,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(1580,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1676,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_List_Omember ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).
thf(1619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_List_Omember ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_HOL_Oord )
| ~ ( A @ class_Int_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__number__of_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
| ~ ( A @ class_HOL_Oord )
| ~ ( A @ class_Int_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
thf(665,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1656,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(294,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0L_0) ).
thf(1195,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(378,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(1392,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(455,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__replicate_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__take_0) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(468,axiom,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omember ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I1_J_0) ).
thf(1602,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omember ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(264,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(1128,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__rev_0) ).
thf(1259,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(1328,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(1375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_0) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
thf(697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(874,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(1143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_1) ).
thf(1498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
thf(1567,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(1292,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(1461,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(1424,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(637,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(1644,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
thf(1419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(169,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(901,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(686,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(1612,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__take_0) ).
thf(970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
thf(1099,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(1456,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
thf(1131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(1552,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(293,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1192,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(984,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(721,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(212,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(1002,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1429,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(512,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Onchotomy_0) ).
thf(1715,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(115,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(779,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_b____ @ c_List_Olist_OCons ) ) @ ( v_a____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(515,plain,
! [A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_b____ @ c_List_Olist_OCons ) ) @ ( v_a____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(1249,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Oreplicate ) ) )
= ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(1231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Oreplicate ) ) )
= ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(1627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1525,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(504,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(1695,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( B
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
= ( D @ ( A @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__list__update_1) ).
thf(1170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( B
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
= ( D @ ( A @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(430,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I2_J_1) ).
thf(1515,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Otake ) ) )
= ( C @ ( B @ ( A @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__butlast_0) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Otake ) ) )
= ( C @ ( B @ ( A @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(7,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(530,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(191,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(953,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(180,axiom,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(926,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( D @ ( A @ ( B @ c_Suc @ c_List_Odrop ) ) @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ ( B @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).
thf(1202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( D @ ( A @ ( B @ c_Suc @ c_List_Odrop ) ) @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ ( B @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Orev ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_List_Orev ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__update_0) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Orev ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_List_Orev ) @ c_List_Olist__update ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(110,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(765,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(511,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1712,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
thf(662,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
= ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
| ( C
!= ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A )
| ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
= ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
| ( C
!= ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A )
| ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(418,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1483,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(328,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(1273,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(1548,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(745,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(601,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(1251,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(340,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(1301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(1595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__drop_0) ).
thf(1154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(694,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
thf(732,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__CHAINED__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1389,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__CHAINED__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(843,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(101,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(743,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(193,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(958,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(136,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(826,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__replicate_0) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1488,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(641,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Obutlast ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__butlast_0) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Obutlast ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(1271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(480,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(1635,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(1058,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(250,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append1_0) ).
thf(1092,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
!= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
!= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(125,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(804,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(409,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(1464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__take_0) ).
thf(979,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
thf(1282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(434,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(1524,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__append_0) ).
thf(736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xthird__alt__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_third__alt_0) ).
thf(1492,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xthird__alt__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(1542,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(23,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(567,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(1408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
thf(784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
thf(1589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(990,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1571,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(398,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(1439,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(493,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(1667,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(1471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(52,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(631,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(108,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(758,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(535,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(478,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(1630,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(700,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(1325,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__tl_0) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__Suc_0) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1556,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff_0) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Ohd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(1381,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Ohd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(501,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1688,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Osplice ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__splice_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Osplice ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).
thf(1015,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(1435,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(1477,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__drop_0) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(653,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(178,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(922,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(174,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append_0) ).
thf(912,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc_0) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(1044,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(316,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(1245,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(1445,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(436,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(1528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
thf(1113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(563,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oexhaust_0) ).
thf(1413,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(226,axiom,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1034,plain,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(341,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(1304,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(1467,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(548,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(754,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Int_Onumber )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1049,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(459,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(1583,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(8,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(531,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= B )
| ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__id_0) ).
thf(812,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= B )
| ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ c_List_Olist_ONil ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ c_List_Olist_ONil ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(1145,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(219,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(1018,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__drop_0) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(150,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(855,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__take_0) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(872,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__list__update_0) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(485,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__take_0) ).
thf(1647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) @ c_List_Otl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__tl_0) ).
thf(712,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) @ c_List_Otl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Orderings_Oord__class_Omin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__take_0) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Orderings_Oord__class_Omin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(1598,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(707,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(840,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1235,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(498,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
thf(1218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
thf(1220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(13,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(544,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__take_0) ).
thf(1186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(228,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1038,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(1085,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(27,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(576,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1658,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(1538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(951,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(1023,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(1284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(362,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(1353,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(1504,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).
thf(1670,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1008,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(571,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(44,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(612,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(859,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(1240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(383,axiom,
! [A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_b____ @ c_List_Olist_OCons ) ) @ ( v_a____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(1404,plain,
! [A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_b____ @ c_List_Olist_OCons ) ) @ ( v_a____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(438,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(1536,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(1052,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(845,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(486,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(1649,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_0) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(349,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(1321,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__replicate_0) ).
thf(891,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1126,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__drop_0) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(500,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(1685,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(688,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(170,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(903,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(588,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(1062,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1481,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(254,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(1101,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).
thf(781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
= ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(1674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
= ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(1639,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(24,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(568,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(343,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(1308,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1661,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(279,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(1161,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(473,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( D @ ( C @ ( B @ ( D @ ( A @ c_List_Obutlast ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__list__update_1) ).
thf(1133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( D @ ( C @ ( B @ ( D @ ( A @ c_List_Obutlast ) @ c_List_Olist__update ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
thf(1348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(1512,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
= C )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__list__update_0) ).
thf(833,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
= C )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(1097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(1593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(272,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0R_0) ).
thf(1148,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(999,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(1395,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(1363,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
thf(807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__conv__mod_0) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1165,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(503,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(1693,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(1410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
= C )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
= C )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Obutlast ) )
= ( B @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__conv__take_0) ).
thf(1288,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Obutlast ) )
= ( B @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(1710,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(987,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons__number__of_1) ).
thf(1261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(326,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1268,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons__number__of_1) ).
thf(723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(1399,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(1550,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(208,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(992,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1606,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
thf(1653,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
= ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
= ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(388,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(639,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(200,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_expand__Suc_0) ).
thf(972,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1490,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
thf(560,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1725,plain,
$false,
inference(e,[status(thm)],[1322,1036,1469,1190,760,1454,1633,1559,846,628,893,1179,777,1295,1501,809,1337,1718,1315,518,1083,962,1554,1110,1200,977,1211,1158,1005,1406,683,1522,1443,994,1569,1205,1591,1533,677,1437,1173,730,1290,878,655,1041,861,1705,1426,1671,1310,797,1275,1233,747,538,670,1507,1222,1441,709,1046,1386,1475,565,1254,651,829,1095,1518,1703,1298,838,802,1313,1577,934,949,1330,1264,917,702,751,1545,817,559,853,1379,1087,1247,770,881,1115,1641,1319,870,1479,1609,924,789,1450,591,1373,646,514,966,1183,756,1664,1682,1136,1383,1020,981,1377,1215,692,734,1072,1622,660,1433,1600,527,1564,1447,956,1697,1242,849,1651,942,1306,1708,1067,714,1636,1163,1074,1604,910,1343,1042,598,820,815,1238,1355,1580,1123,862,1174,1676,1619,1370,1365,625,665,583,1159,1656,1027,1195,1392,1573,1012,1032,1602,551,1128,1402,1259,1328,1375,1227,1540,593,610,1360,1350,697,1089,874,1143,1498,1587,857,1397,1567,1292,554,1461,1424,637,1700,1207,1644,1419,901,686,1612,679,970,622,1099,738,1456,1131,1552,1192,1060,984,721,1002,1429,1715,779,605,515,1150,1249,1266,1231,1627,1525,1333,805,1695,541,657,1170,1286,1515,1167,530,953,926,1202,792,765,1712,1054,662,718,888,906,1103,824,1483,1273,1548,745,573,601,1251,618,1301,1595,1154,975,694,732,1389,843,772,743,579,958,1520,826,577,1256,545,1488,641,1139,936,1271,1635,1058,1092,704,919,804,1464,947,979,1209,831,1282,1524,736,1492,1542,567,649,616,1690,681,1408,784,1117,1589,990,996,1571,599,1439,1667,1471,1080,631,758,535,1630,726,700,1325,964,915,1556,668,1381,1688,1029,895,883,1015,1435,1477,851,653,922,1562,912,521,1213,827,1044,1245,1445,1528,1176,608,1113,563,1413,1034,1304,1467,795,548,1277,749,754,836,1049,675,1583,531,944,812,1509,939,1340,1145,1018,968,1181,855,1025,872,1156,1647,1368,712,557,1003,690,1598,1225,707,673,1452,840,1235,1317,1679,1218,1220,544,1188,1186,1038,585,1085,576,1658,1538,951,1023,613,1284,1353,1504,1585,1670,1008,571,595,612,876,859,1240,1404,1358,1141,1536,1485,1052,845,1421,1649,1459,1321,891,1126,1108,931,1685,688,903,524,581,1010,1575,588,1062,1481,1101,632,786,781,1674,1639,568,1308,1077,899,1661,716,1161,1614,800,1133,1348,1512,1280,833,1097,1229,818,1593,1148,865,603,999,620,1395,1625,1363,1495,807,1056,532,1165,1346,928,1335,1693,897,1410,767,1288,1710,1197,960,635,1473,987,1261,1268,1152,723,822,1431,1399,1120,728,740,644,1550,908,992,1606,1653,1565,1416,639,1069,972,1490,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT042-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/10.52 % Computer : n001.cluster.edu
% 0.23/10.52 % Model : x86_64 x86_64
% 0.23/10.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/10.52 % Memory : 8046.5625MB
% 0.23/10.52 % OS : Linux 6.8.0-71-generic
% 0.23/10.52 % CPULimit : 300
% 0.23/10.52 % WCLimit : 300
% 0.23/10.52 % DateTime : Sat Sep 26 06:27:22 UTC 2026
% 0.23/10.52 % CPUTime :
% 0.23/10.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.51/11.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.07/11.99 % [INFO] Parsing done (580ms).
% 3.07/12.01 % [INFO] Running in sequential loop mode.
% 4.80/12.60 % [INFO] eprover registered as external prover.
% 4.80/12.61 % [INFO] Scanning for conjecture ...
% 5.50/12.90 % [INFO] Found a conjecture (or negated_conjecture) and 664 axioms. Running axiom selection ...
% 6.91/13.25 % [INFO] Axiom selection finished. Selected 511 axioms (removed 153 axioms).
% 8.67/13.62 % [INFO] Problem is propositional (TPTP CNF).
% 8.67/13.66 % [INFO] Type checking passed.
% 8.67/13.66 % [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 ...
% 22.46/17.08 % External prover 'e' found a proof!
% 22.46/17.08 % [INFO] Killing All external provers ...
% 22.46/17.08 % Time passed: 6342ms (effective reasoning time: 5065ms)
% 22.46/17.09 % Axioms used in derivation (511): clsarity_nat__HOL_Oord, cls_Nil__is__rev__conv_1, cls_not__one__less__zero_0, cls_last_Osimps_0, cls_min__max_Oinf__commute_0, cls_linorder__antisym__conv2_1, cls_power__0_0, cls_natgb_Oadd__r0__iff_1, cls_min__max_Ole__infE_0, cls_length__0__conv_1, cls_take__eq__Nil_0, cls_take__take_0, cls_butlast__snoc_0, cls_Suc__pred_0, cls_last__drop_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_order__le__less__trans_0, cls_min__max_Oless__infI1_0, cls_rev__swap_1, cls_add__is__1_1, cls_last_Osimps_1, cls_zero__less__one_0, cls_Cons__eq__append__conv_2, cls_Suc__inject_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_Suc__mono_0, cls_Cons__eq__append__conv_5, cls_remove1_Osimps_I2_J_0, cls_list__update__overwrite_0, cls_splice_Osimps_I2_J_1, cls_xt1_I12_J_0, cls_append__self__conv_0, cls_Suc__n__not__n_0, cls_min__max_Oinf__le1_0, cls_zero__le__one_0, cls_take__tl_0, cls_butlast_Osimps_I1_J_0, cls_one__is__add_4, cls_drop__append_0, cls_min__less__iff__conj_0, cls_distinct__remove1__removeAll_0, cls_nat__add__left__cancel__less_1, cls_splice__Cons__Cons_0, cls_take__0_0, cls_diff__Suc__1_0, cls_list_Oinject_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_tl_Osimps_I1_J_0, cls_linorder__neqE_0, cls_less__antisym_0, cls_CHAINED_0, cls_less__add__Suc2_0, cls_take__Cons_H_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_min__0R_0, cls_replicate__empty_0, cls_rev__singleton__conv_1, cls_pos__add__strict_0, cls_termination__basic__simps_I1_J_0, cls_add__is__0_0, cls_not__Cons__self2_0, cls_Suc__lessI_0, cls_diff__cancel_0, cls_removeAll_Osimps_I2_J_0, cls_min__less__iff__disj_2, cls_not__less__eq_1, cls_rev__is__rev__conv_0, cls_one__is__add_1, clsarity_nat__Orderings_Olinorder, cls_list__update__append_1, cls_less__Suc__eq_2, cls_nat__add__left__cancel__less_0, cls_min__less__iff__disj_0, cls_distinct__rev_1, cls_append__eq__append__conv__if_6, cls_list__update__nonempty_1, cls_eq__Nil__appendI_0, cls_order__less__trans_0, cls_self__append__conv_0, cls_alt3_0, cls_power__less__imp__less__exp_0, cls_length__splice_0, cls_drop__0_0, cls_power__gt1_0, cls_append__eq__Cons__conv_4, cls_List_Omember_Osimps_I2_J_0, cls_same__append__eq_0, cls_take__Cons__number__of_1, cls_append__Cons_0, cls_butlast_Osimps_I2_J_1, cls_gr0I_0, cls_rotate__conv__mod_0, cls_length__butlast_0, cls_add__gr__0_0, cls_hd__append_0, cls_drop__Cons__number__of_0, cls_replicate__eq__replicate_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_diff__diff__left_0, cls_append__eq__Cons__conv_0, cls_min__max_Oless__infI2_0, cls_min__number__of_1, cls_one__le__power_0, cls_tl__replicate_0, cls_gr__implies__not0_0, cls_sorted_Osimps_I3_J_1, cls_linorder__not__less_0, cls_list_Osize_I4_J_0, cls_add__less__mono_0, cls_rev__drop_0, cls_rev__take_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_min__max_Ole__inf__iff_1, cls_order__less__asym_0, cls_butlast__list__update_0, cls_mod__if_1, cls_append1__eq__conv_1, cls_order__eq__refl_0, cls_neq__Nil__conv_0, cls_order__le__less_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_splice_Osimps_I2_J_0, cls_linorder__antisym__conv2_0, cls_distinct_Osimps_I1_J_0, cls_linorder__antisym__conv1_0, cls_sorted__take_0, cls_distinct_Osimps_I2_J_1, cls_length__greater__0__conv_1, cls_empty__null_0, cls_min__max_Ole__infE_1, cls_length__remdups__eq_0, cls_replicate__append__same_0, cls_rev_Osimps_I2_J_0, cls_add__Suc_0, cls_hd__append_1, cls_list__update__append1_0, cls_distinct__remove1_0, cls_take__1__Cons_0, cls_drop__Suc__Cons_0, cls_rev__singleton__conv_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_less__le__not__le_2, cls_diff__add__inverse2_0, cls_xt1_I10_J_0, cls_append__Nil2_0, cls_rotate__rev_0, cls_nat__add__left__commute_0, cls_not__less__iff__gr__or__eq_0, cls_diff__Suc__Suc_0, cls_append__self__conv2_0, cls_remdups__id__iff__distinct_0, cls_one__is__add_5, cls_class__semiring_Osemiring__rules_I6_J_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_rotate__is__Nil__conv_0, cls_self__append__conv2_0, cls_drop__tl_0, cls_CHAINED_0_01, cls_distinct__append_0, cls_power__0__Suc_0, cls_remdups__eq__nil__iff_1, cls_Cons__eq__append__conv_3, cls_self__append__conv2_1, cls_sorted__drop_0, cls_rotate__rotate_0, cls_sorted_Osimps_I3_J_2, cls_Suc__diff__1_0, cls_removeAll__append_0, cls_length__0__conv_0, cls_mod__Suc_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_min__max_Ole__infI2_0, cls_append__is__Nil__conv_2, cls_append__Nil_0, cls_one__is__add_0, cls_append__eq__append__conv2_5, cls_list_Oexhaust_0, cls_less__add__Suc1_0, cls_rev__update_0, cls_take__Cons_H_1, cls_append__eq__Cons__conv_5, cls_replicate__Suc_0, cls_List_Omember_Osimps_I2_J_1, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_length__list__update_0, cls_add__is__1_0, cls_length__take_0, cls_class__semiring_Oadd__a_0, cls_last__append_1, cls_min__max_Ole__iff__inf_1, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_xt1_I8_J_0, cls_drop__Cons__number__of_1, cls_List_Omember_Osimps_I1_J_0, cls_min__max_Oinf__assoc_0, cls_rev__is__Nil__conv_0, cls_distinct__rev_0, cls_butlast__conv__take_0, cls_min__max_Oinf__idem_0, cls_class__semiring_Oadd__0_0, cls_min__max_Ole__inf__iff_0, cls_butlast__list__update_1, cls_last__list__update_1, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_take__hd__drop_0, cls_length__remdups__eq_1, cls_distinct__rotate_1, cls_replicate__app__Cons__same_0, cls_power__strict__mono_0, cls_min__max_Oinf__left__idem_0, cls_rotate__simps_0, cls_replicate__eq__replicate_1, cls_One__nat__def_0, cls_lessI_0, cls_power__strict__decreasing_0, cls_drop__1__Cons_0, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_diff__Suc__eq__diff__pred_0, cls_zero__less__two_0, cls_less__add__one_0, cls_not__leE_0, cls_min__le__iff__disj_0, cls_append__eq__Cons__conv_1, cls_list__update__append_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_splice__Nil2_0, cls_zero__less__power_0, cls_order__antisym_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_butlast__append_0, cls_less__add__eq__less_0, cls_list__update__code_I2_J_0, cls_le__number__of__eq__not__less_1, cls_self__append__conv_1, cls_take__append_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_append__eq__conv__conj_2, cls_less__Suc__eq__0__disj_3, cls_rotate1__is__Nil__conv_0, cls_rotate1__rotate__swap_0, cls_not__Cons__self_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_linorder__antisym__conv1_1, cls_length__greater__0__conv_0, cls_append__same__eq_0, cls_last__snoc_0, cls_append__take__drop__id_0, cls_splice_Osimps_I1_J_0, cls_last__append_0, cls_zero__neq__one_0, cls_list__update__swap_0, cls_length__rev_0, cls_append__eq__conv__conj_0, cls_rotate__drop__take_0, cls_butlast__drop_0, cls_less__imp__diff__less_0, cls_natgb_Oadd__cancel_0, cls_drop__Cons_H_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_diff__less_0, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_distinct1__rotate_0, cls_linorder__not__le_1, cls_append__assoc_0, cls_one__is__add_2, cls_not__less__less__Suc__eq_0, cls_butlast__append_1, cls_tl__take_0, cls_mod__Suc_1, cls_drop__Nil_0, cls_neq0__conv_1, cls_add__Suc__right_0, cls_not__less__iff__gr__or__eq_1, cls_Cons__eq__append__conv_0, cls_drop__butlast_0, cls_Nitpick_Olist__size__simp_I2_J_1, cls_nat__add__right__cancel_0, cls_mod__1_0, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, clsarity_nat__Int_Onumber, cls_order__le__neq__trans_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_diff__less__Suc_0, cls_less__not__refl_0, cls_linorder__antisym__conv3_0, cls_last__rev_0, cls_min__max_Oinf__greatest_0, cls_rotate__Suc_0, cls_removeAll_Osimps_I1_J_0, cls_gr0__conv__Suc_1, cls_list_Onchotomy_0, cls_less__le__not__le_1, cls_take__eq__Nil_2, cls_distinct__append_1, cls_last__list__update_0, cls_order__eq__iff_2, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_sorted__remdups_0, cls_less__diff__conv_1, cls_rotate__id_0, cls_less__diff__conv_0, cls_order__antisym__conv_0, cls_rev__replicate_0, cls_less__SucE_0, cls_order__neq__le__trans_0, cls_power__eq__imp__eq__base_0, cls_distinct__remdups__id_0, cls_empty__replicate_0, cls_remdups__eq__nil__right__iff_1, cls_append__eq__Cons__conv_2, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_replicate__add_0, cls_sorted_Osimps_I1_J_0, cls_tl__append2_0, cls_nat_Oinject_0, cls_add__lessD1_0, cls_sorted__remove1_0, cls_rotate__simps_1, cls_List_Onull_Osimps_I2_J_0, cls_drop__drop_0, cls_rev__eq__Cons__iff_1, cls_hd__replicate_0, cls_power__le__imp__le__base_0, cls_not__less__less__Suc__eq_1, clsarity_nat__Power_Opower, cls_drop__replicate_0, cls_rotate__is__Nil__conv_1, cls_Nat_Oadd__0__right_0, cls_min__max_Ole__infI1_0, cls_power__strict__increasing__iff_1, cls_sorted__append_0, cls_linorder__less__linear_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_Suc__lessD_0, cls_order__less__le_2, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_drop__Suc_0, cls_Suc__length__conv_2, cls_add__is__1_4, cls_add__is__1_5, cls_rotate1__hd__tl_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_append__eq__conv__conj_1, cls_xt1_I11_J_0, cls_one__neq__zero_0, cls_add__eq__if_1, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_rev__is__Nil__conv_1, cls_natgb_Oadd__r0__iff_0, cls_min__Suc__Suc_0, cls_length__append_0, cls_last__replicate_0, cls_length__rotate1_0, cls_diff__self__eq__0_0, cls_take__Suc__Cons_0, cls_less__Suc0_0, cls_length__rotate_0, cls_min__max_Ole__inf__iff_2, cls_xt1_I6_J_0, cls_diff__Suc__less_0, cls_min__max_Oinf__le2_0, cls_replicate__eq__replicate_2, cls_min__less__iff__conj_2, cls_distinct__rotate_0, cls_take__butlast_0, cls_append__is__Nil__conv_1, cls_take__replicate_0, cls_nat_Osimps_I3_J_0, cls_plus__nat_Oadd__0_0, cls_length__drop_0, cls_min__max_Oinf__absorb2_0, cls_linorder__not__le_0, cls_Cons__eq__appendI_0, cls_min__max_Oinf__left__commute_0, cls_diff__less__mono2_0, cls_length__tl_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_less__trans__Suc_0, cls_Nil__is__rev__conv_0, cls_order__less__irrefl_0, cls_Cons__eq__append__conv_4, cls_append__is__Nil__conv_0, cls_add__is__0_2, cls_distinct__take_0, cls_class__semiring_Oadd__c_0, cls_singleton__rev__conv_1, cls_append__eq__appendI_0, cls_one__less__power_0, cls_power__Suc__less__one_0, cls_nat__add__left__cancel_0, cls_minus__nat_Odiff__0_0, cls_butlast_Osimps_I2_J_0, cls_add__is__1_3, cls_length__Suc__conv_2, cls_diff__0__eq__0_0, cls_list_Oinject_1, cls_zero__less__diff_1, cls_distinct__remdups_0, cls_add__eq__self__zero_0, cls_power__less__imp__less__base_0, cls_hd_Osimps_0, cls_mod__less__divisor_0, cls_Suc__eq__plus1_0, cls_rev__append_0, cls_n__not__Suc__n_0, cls_min__le__iff__disj_1, cls_Cons__eq__append__conv_1, cls_take__Cons__number__of_0, cls_min__le__iff__disj_2, cls_remove1_Osimps_I2_J_1, cls_power__inject__base_0, cls_min__max_Ole__infI_0, cls_less__SucI_0, cls_drop__take_0, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_not__less0_0, cls_hd__rev_0, cls_diffs0__imp__equal_0, cls_expand__Suc_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_rev__swap_0, cls_tl__drop_0, cls_min__max_Ole__iff__inf_0, cls_replicate__empty_1, cls_one__is__add_3, cls_sorted_Osimps_I2_J_0, cls_List_Omember_Osimps_I2_J_2, cls_diff__add__inverse_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_tl_Osimps_I2_J_0, cls_class__semiring_Opwr__0_0, cls_Suc__less__eq_0, cls_length__replicate_0, cls_add__gr__0_2, cls_zero__le__power_0, cls_third__alt_0, cls_take__drop_0, cls_order__less__imp__le_0, cls_take__Suc_0, cls_distinct__drop_0, cls_min__number__of_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_that_0, cls_Suc__pred_H_0, cls_add__gr__0_1, cls_diff__commute_0, cls_power__strict__increasing__iff_0, cls_mod__if_0, cls_less__Suc0_1, cls_termination__basic__simps_I2_J_0, cls_Suc__eq__plus1__left_0, cls_append__eq__Cons__conv_3, cls_list__update__code_I3_J_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_remdups__eq__nil__iff_0, cls_linorder__not__less_1, cls_removeAll_Osimps_I2_J_1, cls_nat__less__le_1, cls_min__diff_0, cls_upd__conv__take__nth__drop_0, cls_rev__rev__ident_0, cls_distinct1__rotate_1, cls_empty__replicate_1, cls_sorted_Osimps_I3_J_0, cls_min__less__iff__conj_1, cls_xt1_I7_J_0, cls_zero__less__Suc_0, cls_append1__eq__conv_0, cls_drop__Cons_H_1, cls_not__one__le__zero_0, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_min__less__iff__disj_1, cls_min__0L_0, cls_power__0__left_1, cls_mod__Suc__eq__Suc__mod_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_le__number__of__eq__not__less_0, cls_list__update__nonempty_0, cls_power__mono_0, cls_add__diff__inverse_0, cls_empty__null_1
% 22.46/17.09 % No. of inferences in proof: 1027
% 22.46/17.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6342 ms resp. 5065 ms w/o parsing
% 24.29/17.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.29/17.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------