TSTP Solution File: ANA042-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA042-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:08:58 EDT 2023
% Result : Unsatisfiable 10.82s 3.49s
% Output : Refutation 11.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 865
% Syntax : Number of formulae : 1639 ( 397 unt; 92 typ; 0 def)
% Number of atoms : 3193 ( 726 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 13062 (1584 ~;1646 |; 0 &;9832 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 14 con; 0-3 aty)
% Number of variables : 2700 ( 0 ^;2700 !; 0 ?;2700 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(v_h_type,type,
v_h: $i > $i > $i ).
thf(t_c_type,type,
t_c: $i ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_f_type,type,
v_f: $i > $i > $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_xb_type,type,
v_xb: $i > $i ).
thf(v_A_type,type,
v_A: $i > $i ).
thf(v_xa_type,type,
v_xa: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(class_LOrder_Ojoin__semilorder_type,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_IntDef_Oint_type,type,
c_IntDef_Oint: $i > $i ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(c_UNIV_type,type,
c_UNIV: $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_OrderedGroup_Olordered__ab__group_type,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
thf(c_LOrder_Omeet_type,type,
c_LOrder_Omeet: $i > $i > $i > $i ).
thf(c_LOrder_Ojoin_type,type,
c_LOrder_Ojoin: $i > $i > $i > $i ).
thf(c_Nat_Opower_type,type,
c_Nat_Opower: $i > $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_IntDef_Oneg_type,type,
c_IntDef_Oneg: $i > $i > $o ).
thf(c_Numeral_Onumber__of_type,type,
c_Numeral_Onumber__of: $i > $i > $i ).
thf(c_Divides_Oop_Amod_type,type,
c_Divides_Oop_Amod: $i > $i > $i > $i ).
thf(c_div_type,type,
c_div: $i > $i > $i > $i ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_type,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_1_type,type,
c_1: $i ).
thf(class_Power_Orecpower_type,type,
class_Power_Orecpower: $i > $o ).
thf(c_Parity_Oeven_type,type,
c_Parity_Oeven: $i > $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1__cancel_type,type,
class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).
thf(c_NatArith_Oof__nat_type,type,
c_NatArith_Oof__nat: $i > $i > $i ).
thf(c_IntDef_Onat_type,type,
c_IntDef_Onat: $i > $i ).
thf(class_LOrder_Omeet__semilorder_type,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_type,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(c_IntDef_Oof__int_type,type,
c_IntDef_Oof__int: $i > $i > $i ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_HOL_Otimes_type,type,
class_HOL_Otimes: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_type,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_SetInterval_OgreaterThanLessThan_type,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(class_LOrder_Olorder_type,type,
class_LOrder_Olorder: $i > $o ).
thf(c_SetInterval_OatLeastAtMost_type,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0__cancel_type,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__meet_type,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__join_type,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(c_SetInterval_OgreaterThanAtMost_type,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_type,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
thf(c_SetInterval_OatLeast_type,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_SetsAndFunctions_Oelt__set__times_type,type,
c_SetsAndFunctions_Oelt__set__times: $i > $i > $i > $i ).
thf(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_IntDef_OInts_type,type,
c_IntDef_OInts: $i ).
thf(class_Ring__and__Field_Oaxclass__abs__if_type,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
thf(c_List_Ochar_OChar_type,type,
c_List_Ochar_OChar: $i > $i > $i ).
thf(c_OrderedGroup_Onprt_type,type,
c_OrderedGroup_Onprt: $i > $i > $i ).
thf(c_OrderedGroup_Opprt_type,type,
c_OrderedGroup_Opprt: $i > $i > $i ).
thf(c_SetInterval_OgreaterThan_type,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_IntDef_ONats_type,type,
c_IntDef_ONats: $i ).
thf(c_HOL_Oinverse_type,type,
c_HOL_Oinverse: $i > $i > $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_type,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Oall__not__in__conv__1_type,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_Main_Omod__eq__0D__dest__1_type,type,
c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).
thf(c_Main_Ozmod__eq__0D__dest__1_type,type,
c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).
thf(c_List_Olexn_type,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Ochar_type,type,
tc_List_Ochar: $i ).
thf(670,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ B @ c_1 @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
thf(2199,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ B @ c_1 @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
thf(1411,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(315,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(1469,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(712,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(2295,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(445,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(1729,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
thf(846,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(524,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(1899,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ A @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ A @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
thf(962,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(3,negated_conjecture,
! [A: $i] : ( c_in @ ( v_xb @ A ) @ ( v_A @ ( v_xa @ A ) ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(777,plain,
! [A: $i] : ( c_in @ ( v_xb @ A ) @ ( v_A @ ( v_xa @ A ) ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
thf(1586,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( ( c_LOrder_Ojoin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
thf(809,plain,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( ( c_LOrder_Ojoin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ C @ tc_nat )
= ( c_minus @ ( c_Suc @ B ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ C @ tc_nat )
= ( c_minus @ ( c_Suc @ B ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(439,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
thf(1718,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(267,axiom,
class_Orderings_Oorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(1369,plain,
class_Orderings_Oorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(487,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
thf(1190,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(728,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(2336,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ~ ( c_in @ B @ c_IntDef_ONats @ A )
| ~ ( c_in @ C @ c_IntDef_ONats @ A )
| ( c_in @ ( c_plus @ C @ B @ A ) @ c_IntDef_ONats @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ~ ( c_in @ B @ c_IntDef_ONats @ A )
| ~ ( c_in @ C @ c_IntDef_ONats @ A )
| ( c_in @ ( c_plus @ C @ B @ A ) @ c_IntDef_ONats @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(307,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(1454,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( c_in @ ( c_NatArith_Oof__nat @ B @ A ) @ c_IntDef_ONats @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
thf(2031,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( c_in @ ( c_NatArith_Oof__nat @ B @ A ) @ c_IntDef_ONats @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(606,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
thf(2072,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
thf(1767,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(568,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(1995,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(698,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
thf(2263,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(116,axiom,
! [A: $i] :
~ ( c_lessequals @ c_0 @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
thf(1031,plain,
! [A: $i] :
~ ( c_lessequals @ c_0 @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(56,axiom,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(893,plain,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(494,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_22) ).
thf(1840,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(484,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
thf(1818,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
thf(1295,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(548,axiom,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(1950,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(357,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(1549,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(718,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(1068,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(343,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(1522,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
thf(1618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(134,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ c_0 @ c_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
thf(1073,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ c_0 @ c_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(355,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
thf(1544,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(473,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
thf(1793,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(237,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(1305,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(502,axiom,
class_HOL_Otimes @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
thf(1855,plain,
class_HOL_Otimes @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(609,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ D @ E @ A )
| ( c_in @ ( c_times @ D @ B @ A ) @ ( c_times @ E @ C @ ( tc_set @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro_0) ).
thf(2077,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ D @ E @ A )
| ( c_in @ ( c_times @ D @ B @ A ) @ ( c_times @ E @ C @ ( tc_set @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(536,axiom,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
thf(1924,plain,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
thf(1005,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(675,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(2210,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
thf(2117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(380,axiom,
class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(1596,plain,
class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(1882,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(302,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(1443,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(479,axiom,
class_Orderings_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(1808,plain,
class_Orderings_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(292,axiom,
! [A: $i] :
( ( c_div @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
thf(1422,plain,
! [A: $i] :
( ( c_div @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(543,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(1939,plain,
class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
thf(873,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= ( c_Nat_Opower @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
thf(2099,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= ( c_Nat_Opower @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(377,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(1591,plain,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(627,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ E @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_times @ D @ B @ ( tc_set @ A ) ) @ ( c_times @ E @ C @ ( tc_set @ A ) ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono2_0) ).
thf(2114,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ E @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_times @ D @ B @ ( tc_set @ A ) ) @ ( c_times @ E @ C @ ( tc_set @ A ) ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(221,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
thf(1269,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_minus @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_minus @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_lessequals @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
thf(1608,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_lessequals @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
| ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
thf(1655,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
| ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( C = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( C = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(447,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(1735,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(663,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_2) ).
thf(2184,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_plus @ B @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
= ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_plus @ B @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
= ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
thf(1260,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(564,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
thf(1988,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_minus @ B @ C @ tc_IntDef_Oint ) @ A )
= ( c_minus @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_minus @ B @ C @ tc_IntDef_Oint ) @ A )
= ( c_minus @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ B @ C @ tc_nat )
| ~ ( c_less @ c_1 @ D @ A )
| ( c_less @ ( c_Nat_Opower @ D @ B @ A ) @ ( c_Nat_Opower @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
thf(1640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ B @ C @ tc_nat )
| ~ ( c_less @ c_1 @ D @ A )
| ( c_less @ ( c_Nat_Opower @ D @ B @ A ) @ ( c_Nat_Opower @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
thf(945,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(130,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
thf(1063,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(644,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).
thf(2146,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
thf(1458,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(668,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
thf(2195,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(432,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(1705,plain,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(174,axiom,
! [A: $i] :
( ( c_IntDef_Oint @ ( c_Suc @ A ) )
= ( c_plus @ c_1 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
thf(1164,plain,
! [A: $i] :
( ( c_IntDef_Oint @ ( c_Suc @ A ) )
= ( c_plus @ c_1 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(769,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(2434,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(511,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
thf(1872,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(336,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(1507,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_emptyset @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(739,axiom,
! [B: $i,A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= ( c_times @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(2360,plain,
! [B: $i,A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= ( c_times @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(829,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(492,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
thf(1835,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ B @ C @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).
thf(2216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ B @ C @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(733,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
thf(2348,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(2046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
thf(1391,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ C @ A ) @ B @ A )
= ( c_uminus @ ( c_Nat_Opower @ C @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ C @ A ) @ B @ A )
= ( c_uminus @ ( c_Nat_Opower @ C @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(383,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
thf(1601,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(612,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(2082,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(657,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
thf(2173,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(347,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(1529,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(518,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(1887,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(768,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ~ ( c_in @ B @ c_IntDef_ONats @ A )
| ~ ( c_in @ C @ c_IntDef_ONats @ A )
| ( c_in @ ( c_times @ C @ B @ A ) @ c_IntDef_ONats @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
thf(2432,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ~ ( c_in @ B @ c_IntDef_ONats @ A )
| ~ ( c_in @ C @ c_IntDef_ONats @ A )
| ( c_in @ ( c_times @ C @ B @ A ) @ c_IntDef_ONats @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(531,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
thf(1914,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(211,axiom,
! [A: $i] :
( ~ ( c_less @ c_1 @ A @ tc_IntDef_Oint )
| ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
thf(1243,plain,
! [A: $i] :
( ~ ( c_less @ c_1 @ A @ tc_IntDef_Oint )
| ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(782,plain,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( c_less @ c_0 @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
thf(2020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( c_less @ c_0 @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(32,axiom,
! [A: $i] :
( ( c_div @ A @ c_1 @ tc_IntDef_Oint )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
thf(841,plain,
! [A: $i] :
( ( c_div @ A @ c_1 @ tc_IntDef_Oint )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
thf(973,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(52,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(885,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(408,axiom,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
thf(1650,plain,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(405,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(1645,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(442,axiom,
class_HOL_Otimes @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).
thf(1724,plain,
class_HOL_Otimes @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(318,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
thf(1475,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(639,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
thf(2136,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(526,axiom,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(1904,plain,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(431,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
thf(1703,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(1228,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
thf(1623,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(397,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(1628,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(127,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(1055,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
thf(1430,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( A = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
thf(1985,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( A = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(459,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(1760,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(729,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(701,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(2269,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(505,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
thf(1860,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(245,axiom,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(1323,plain,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(703,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
thf(2274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Suc @ c_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
thf(802,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Suc @ c_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(1279,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(308,axiom,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(1455,plain,
! [A: $i] :
( ( c_Pow @ c_UNIV @ A )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_plus @ B @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
= ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_plus @ B @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) @ A @ tc_nat )
= ( c_plus @ C @ ( c_div @ B @ A @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(634,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
thf(2126,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( C = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( C = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
= ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
= ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(595,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
thf(2049,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
thf(870,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(320,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
thf(1479,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(108,axiom,
! [A: $i] :
( ( ( c_IntDef_Oint @ A )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
thf(1013,plain,
! [A: $i] :
( ( ( c_IntDef_Oint @ A )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(650,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(2158,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
thf(1773,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(329,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).
thf(1494,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(206,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
thf(1232,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(498,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
thf(1847,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(535,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(1922,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( c_IntDef_Oint @ ( c_plus @ A @ B @ tc_nat ) )
= ( c_plus @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
thf(817,plain,
! [B: $i,A: $i] :
( ( c_IntDef_Oint @ ( c_plus @ A @ B @ tc_nat ) )
= ( c_plus @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(520,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
thf(1892,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(272,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
thf(1379,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(655,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(2169,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(339,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(1514,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(90,axiom,
c_Parity_Oeven @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
thf(969,plain,
c_Parity_Oeven @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_SetsAndFunctions_Oelt__set__times @ D @ B @ A ) @ ( c_SetsAndFunctions_Oelt__set__times @ D @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono_0) ).
thf(1572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_SetsAndFunctions_Oelt__set__times @ D @ B @ A ) @ ( c_SetsAndFunctions_Oelt__set__times @ D @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(450,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
thf(1741,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(881,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(540,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_SetsAndFunctions_Oelt__set__times @ c_1 @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__one__times_0) ).
thf(1931,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_SetsAndFunctions_Oelt__set__times @ c_1 @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(365,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
thf(1568,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_1) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(1778,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(574,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(2007,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(235,axiom,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(1302,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
thf(1373,plain,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ c_1 @ A ) @ B @ A )
= ( c_uminus @ c_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
thf(1828,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ c_1 @ A ) @ B @ A )
= ( c_uminus @ c_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(182,axiom,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(1183,plain,
! [A: $i] :
( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( c_times @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_plus @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( c_times @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_plus @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(437,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(1714,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
thf(2027,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_NatArith_Oof__nat @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
thf(1109,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_NatArith_Oof__nat @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_IntDef_Oint )
| ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
thf(1632,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_IntDef_Oint )
| ( c_less @ A @ ( c_plus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(290,axiom,
( c_1
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(1418,plain,
( c_1
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(687,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(504,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(507,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(1864,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(632,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
thf(2122,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(937,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(419,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(1677,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(588,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(2034,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(579,axiom,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(2017,plain,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(61,axiom,
( ( c_IntDef_Onat @ c_0 )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
thf(905,plain,
( ( c_IntDef_Onat @ c_0 )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(176,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
thf(1169,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(271,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
thf(1377,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(706,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(2281,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
thf(1215,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
| ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
thf(1447,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
| ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
thf(1394,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(572,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
thf(2002,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(255,axiom,
! [A: $i] : ( c_IntDef_Oneg @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
thf(1345,plain,
! [A: $i] : ( c_IntDef_Oneg @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(752,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(2392,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
thf(2205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(496,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
thf(1843,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(599,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ c_1 @ A ) @ B @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
thf(2058,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ c_1 @ A ) @ B @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(742,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
thf(2367,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(770,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(2437,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
thf(1928,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(522,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(1896,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(517,axiom,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(1886,plain,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
thf(1119,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(393,axiom,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(1622,plain,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(764,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
thf(2424,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(5,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(774,plain,
class_Ring__and__Field_Oordered__idom @ t_c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(622,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
thf(1405,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ ( c_plus @ B @ C @ tc_nat ) @ A )
= ( c_plus @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ ( c_plus @ B @ C @ tc_nat ) @ A )
= ( c_plus @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
thf(1697,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(385,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
thf(1604,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(576,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
thf(2011,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(672,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(2204,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
thf(1691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(925,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(169,axiom,
( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
thf(1153,plain,
( ( c_SetInterval_OlessThan @ c_0 @ tc_nat )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(717,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ C @ ( c_Suc @ ( c_minus @ B @ A @ tc_nat ) ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ A @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
thf(1708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(617,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
thf(2093,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(1868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(748,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(2382,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(600,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
thf(2061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(401,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_13) ).
thf(1636,plain,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
thf(957,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(766,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_in @ B @ C @ A )
| ( c_in @ ( c_times @ D @ B @ A ) @ ( c_SetsAndFunctions_Oelt__set__times @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro2_0) ).
thf(2428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_in @ B @ C @ A )
| ( c_in @ ( c_times @ D @ B @ A ) @ ( c_SetsAndFunctions_Oelt__set__times @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(82,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(952,plain,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(415,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Onprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
thf(1666,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Onprt @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(324,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(1487,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(637,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
thf(2132,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
thf(1560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(276,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_less @ c_0 @ c_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
thf(1387,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_less @ c_0 @ c_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(441,axiom,
class_Power_Orecpower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(1723,plain,
class_Power_Orecpower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(692,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(2249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
thf(1021,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(4,negated_conjecture,
! [A: $i] :
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ A ) @ ( v_xb @ A ) ) @ t_c ) @ ( c_times @ A @ ( v_h @ ( v_xa @ A ) @ ( v_xb @ A ) ) @ t_c ) @ t_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(778,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ A ) @ ( v_xb @ A ) ) @ t_c ) @ ( c_times @ A @ ( v_h @ ( v_xa @ A ) @ ( v_xb @ A ) ) @ t_c ) @ t_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(1355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(371,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(1580,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(156,axiom,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
thf(1123,plain,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
thf(862,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ B ) ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
thf(1570,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(333,axiom,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(1502,plain,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(455,axiom,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
thf(1751,plain,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(10,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
thf(788,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(646,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_NatArith_Oof__nat @ B @ tc_IntDef_Oint ) @ A )
= ( c_NatArith_Oof__nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
thf(2150,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_NatArith_Oof__nat @ B @ tc_IntDef_Oint ) @ A )
= ( c_NatArith_Oof__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( ( c_minus @ B @ ( c_insert @ A @ D @ C ) @ ( tc_set @ C ) )
= ( c_minus @ B @ D @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
thf(1370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( ( c_minus @ B @ ( c_insert @ A @ D @ C ) @ ( tc_set @ C ) )
= ( c_minus @ B @ D @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
thf(1238,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(578,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(2015,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
thf(916,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(534,axiom,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_14) ).
thf(1920,plain,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(309,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
thf(1457,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(603,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).
thf(2068,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ B @ tc_nat ) @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
thf(1210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ C @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= ( c_minus @ ( c_plus @ C @ B @ tc_nat ) @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(285,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(1407,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(731,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(2344,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(529,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ c_1 @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
thf(1910,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ c_1 @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(493,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( B = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
thf(1837,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( B = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
thf(1602,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(556,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
thf(1968,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(879,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ c_1 @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
thf(852,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ c_1 @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(360,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).
thf(1555,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(889,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(660,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(2179,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
thf(1787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(661,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
thf(2181,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( c_times @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_plus @ B @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( c_times @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_plus @ B @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(725,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ B @ c_0 @ A )
= ( c_times @ C @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
thf(2327,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ B @ c_0 @ A )
= ( c_times @ C @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(400,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
thf(1634,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(683,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(2228,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(542,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
thf(1936,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(378,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1592,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
thf(1762,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(500,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ A @ A @ tc_nat )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
thf(1851,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ A @ A @ tc_nat )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(746,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( c_in @ c_0 @ c_IntDef_ONats @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
thf(2377,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( c_in @ c_0 @ c_IntDef_ONats @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
thf(1534,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(477,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
thf(1804,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(557,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
thf(1970,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
thf(1856,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(417,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
thf(1672,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(353,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
thf(1540,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(513,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
thf(1878,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(457,axiom,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
thf(1755,plain,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
thf(857,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(141,axiom,
c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
thf(1089,plain,
c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(207,axiom,
! [A: $i] :
( ( c_NatArith_Oof__nat @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
thf(1234,plain,
! [A: $i] :
( ( c_NatArith_Oof__nat @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(270,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
thf(1375,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(155,axiom,
~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
thf(1121,plain,
~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
!= ( c_IntDef_Oint @ B ) )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
thf(980,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
!= ( c_IntDef_Oint @ B ) )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
| ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
| ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ~ ( c_in @ C @ c_IntDef_OInts @ A )
| ( c_in @ ( c_minus @ C @ B @ A ) @ c_IntDef_OInts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
thf(1683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ~ ( c_in @ C @ c_IntDef_OInts @ A )
| ( c_in @ ( c_minus @ C @ B @ A ) @ c_IntDef_OInts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(248,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
thf(1329,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(172,axiom,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_IntDef_Oint @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
thf(1160,plain,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_IntDef_Oint @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(263,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
thf(1361,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
thf(2323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ B @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
thf(1739,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ B @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(293,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
thf(1424,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(611,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
thf(2080,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(495,axiom,
class_Power_Orecpower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(1842,plain,
class_Power_Orecpower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ( c_in @ ( c_uminus @ B @ A ) @ c_IntDef_OInts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
thf(1791,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ( c_in @ ( c_uminus @ B @ A ) @ c_IntDef_OInts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(734,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
thf(2349,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(590,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
thf(2038,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_0) ).
thf(1889,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(582,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
thf(2023,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(554,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(1964,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(545,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(1942,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(412,axiom,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
thf(1659,plain,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(762,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(2419,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ ( c_plus @ B @ C @ tc_nat ) @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ ( c_plus @ B @ C @ tc_nat ) @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(389,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(1612,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_NatArith_Oof__nat @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).
thf(970,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_NatArith_Oof__nat @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(721,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= ( c_IntDef_Oof__int @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
thf(2317,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= ( c_IntDef_Oof__int @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(170,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
thf(1155,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
thf(837,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(233,axiom,
( ( c_IntDef_Onat @ c_1 )
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
thf(1297,plain,
( ( c_IntDef_Onat @ c_1 )
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(348,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
thf(1530,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(64,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(911,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(547,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(1947,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(562,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
thf(1984,plain,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(1002,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(440,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(1720,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(560,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).
thf(1979,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(2140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ( ( c_NatArith_Oof__nat @ ( c_minus @ C @ B @ tc_nat ) @ A )
= ( c_minus @ ( c_NatArith_Oof__nat @ C @ A ) @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
thf(1114,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ( ( c_NatArith_Oof__nat @ ( c_minus @ C @ B @ tc_nat ) @ A )
= ( c_minus @ ( c_NatArith_Oof__nat @ C @ A ) @ ( c_NatArith_Oof__nat @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
thf(1324,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(708,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(2285,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(466,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
thf(1776,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(102,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
thf(997,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(375,axiom,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(1588,plain,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(1099,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( ( c_minus @ A @ B @ ( tc_set @ C ) )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(97,axiom,
! [A: $i] :
( ( c_HOL_Oabs @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
= ( c_IntDef_Oint @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
thf(985,plain,
! [A: $i] :
( ( c_HOL_Oabs @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
= ( c_IntDef_Oint @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(1266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(647,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(2153,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ C @ B @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
thf(2387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ C @ B @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(737,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(2355,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
thf(1060,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_NatArith_Oof__nat @ B @ A )
!= ( c_NatArith_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_NatArith_Oof__nat @ B @ A )
!= ( c_NatArith_Oof__nat @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(596,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
thf(2052,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ~ ( c_lessequals @ c_1 @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
thf(1599,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ~ ( c_lessequals @ c_1 @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(396,axiom,
c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
thf(1627,plain,
c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(743,axiom,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(2370,plain,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(1525,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(1434,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(192,axiom,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).
thf(1202,plain,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
thf(1241,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
thf(805,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
thf(2043,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
thf(1695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(921,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ~ ( c_in @ C @ c_IntDef_OInts @ A )
| ( c_in @ ( c_plus @ C @ B @ A ) @ c_IntDef_OInts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ~ ( c_in @ C @ c_IntDef_OInts @ A )
| ( c_in @ ( c_plus @ C @ B @ A ) @ c_IntDef_OInts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(608,axiom,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(2076,plain,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
thf(1616,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(569,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_IntDef_Oint )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
thf(1996,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_IntDef_Oint )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
| ( c_less @ A @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
thf(1991,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
| ( c_less @ A @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ B @ C @ tc_nat )
| ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ B @ C @ tc_nat )
| ( c_less @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
thf(1814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(140,axiom,
! [A: $i] :
( ~ ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
thf(1086,plain,
! [A: $i] :
( ~ ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(133,axiom,
( ( c_IntDef_Oint @ c_1 )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
thf(1071,plain,
( ( c_IntDef_Oint @ c_1 )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(756,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(2402,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(414,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(615,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(2089,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(340,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(1515,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(2221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(83,axiom,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
thf(953,plain,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(571,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(2001,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(444,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
thf(1727,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(659,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B = c_0 )
| ( ( c_times @ B @ ( c_HOL_Oinverse @ B @ A ) @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
thf(2176,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B = c_0 )
| ( ( c_times @ B @ ( c_HOL_Oinverse @ B @ A ) @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(552,axiom,
! [A: $i] :
( ~ ( c_less @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
thf(1959,plain,
! [A: $i] :
( ~ ( c_less @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(199,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(1219,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(322,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(1483,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(453,axiom,
( ( c_Suc @ c_0 )
= ( c_times @ c_1 @ c_1 @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
thf(1747,plain,
( ( c_Suc @ c_0 )
= ( c_times @ c_1 @ c_1 @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(214,axiom,
! [A: $i] :
( ( c_SetInterval_OatLeastLessThan @ A @ ( c_Suc @ A ) @ tc_nat )
= ( c_insert @ A @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
thf(1251,plain,
! [A: $i] :
( ( c_SetInterval_OatLeastLessThan @ A @ ( c_Suc @ A ) @ tc_nat )
= ( c_insert @ A @ c_emptyset @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(760,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ A @ C @ tc_nat ) )
| ( B = C )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(2413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ A @ C @ tc_nat ) )
| ( B = C )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(166,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(1146,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(456,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(1754,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(694,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ~ ( c_in @ B @ C @ A )
| ( c_lessequals @ ( c_SetsAndFunctions_Oelt__set__times @ B @ D @ A ) @ ( c_times @ D @ C @ ( tc_set @ A ) ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono4_0) ).
thf(2253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ~ ( c_in @ B @ C @ A )
| ( c_lessequals @ ( c_SetsAndFunctions_Oelt__set__times @ B @ D @ A ) @ ( c_times @ D @ C @ ( tc_set @ A ) ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(587,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(2033,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
thf(819,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
thf(975,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_plus @ ( c_minus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(532,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(1916,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(594,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(2048,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(516,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
thf(1884,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_0) ).
thf(1652,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(283,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
thf(1403,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(342,axiom,
( ( c_SetInterval_OatLeast @ c_0 @ tc_nat )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
thf(1520,plain,
( ( c_SetInterval_OatLeast @ c_0 @ tc_nat )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
thf(2134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( c_less @ c_0 @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
thf(1784,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( c_less @ c_0 @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
thf(1389,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ ( c_HOL_Oabs @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
thf(843,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ ( c_HOL_Oabs @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(157,axiom,
! [A: $i] :
~ ( c_less @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
thf(1125,plain,
! [A: $i] :
~ ( c_less @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(47,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
thf(875,plain,
! [A: $i] : ( c_lessequals @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
thf(826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(474,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
thf(1795,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(430,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(1701,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
thf(1226,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(325,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
thf(1488,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
thf(1428,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(334,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
thf(1503,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_uminus @ B @ tc_IntDef_Oint ) @ A )
= ( c_uminus @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
thf(1669,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_uminus @ B @ tc_IntDef_Oint ) @ A )
= ( c_uminus @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(585,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(2029,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(711,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(222,axiom,
! [A: $i] :
( ( A = c_0 )
| ( ( c_div @ A @ A @ tc_IntDef_Oint )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
thf(1271,plain,
! [A: $i] :
( ( A = c_0 )
| ( ( c_div @ A @ A @ tc_IntDef_Oint )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
thf(1312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
thf(1107,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(772,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(2442,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(143,axiom,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(1092,plain,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(645,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(2148,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(461,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_uminus @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
thf(1765,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_uminus @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_minus @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_minus @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(523,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
thf(1897,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(68,axiom,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(919,plain,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(1464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
thf(947,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(402,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
thf(1638,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(202,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(1224,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(630,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(2119,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(28,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(831,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(286,axiom,
! [A: $i] :
( ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
thf(1408,plain,
! [A: $i] :
( ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(227,axiom,
! [A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
thf(1282,plain,
! [A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(521,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(344,axiom,
c_less @ c_0 @ c_1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
thf(1524,plain,
c_less @ c_0 @ c_1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
thf(1048,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
| ( c_lessequals @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
thf(1542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
| ( c_lessequals @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_IntDef_Oint )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_IntDef_Oint )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(628,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(2116,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(464,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
thf(1771,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(300,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ c_1 @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
thf(1439,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ c_1 @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
= ( c_div @ B @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
= ( c_div @ B @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(732,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(2346,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(610,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(2079,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(719,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= B )
| ( B = c_0 )
| ( C = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
thf(2311,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= B )
| ( B = c_0 )
| ( C = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(613,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
thf(2084,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(677,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(2214,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(8,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_uminus @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
thf(784,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_IntDef_Oint @ A ) @ ( c_uminus @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( c_minus @ A @ c_UNIV @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(368,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(1574,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(478,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(1806,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(107,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(1011,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(376,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).
thf(1589,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(691,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ B @ C @ A )
!= ( c_times @ D @ C @ A ) )
| ( B = D )
| ( C = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).
thf(2246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ B @ C @ A )
!= ( c_times @ D @ C @ A ) )
| ( B = D )
| ( C = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(328,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(1492,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(714,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ c_0 @ B @ A )
= ( c_times @ c_0 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
thf(2299,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ c_0 @ B @ A )
= ( c_times @ c_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
| ( A
= ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) )
| ( A
= ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
thf(1801,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(669,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
thf(2197,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(316,axiom,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
thf(1471,plain,
! [A: $i] :
( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(583,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
thf(2025,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
thf(1557,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(720,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ B @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
thf(2314,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ B @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(625,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
thf(2111,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
thf(1993,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(700,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(2267,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(506,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
thf(1862,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(848,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(759,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
thf(2410,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( c_div @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_div @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
thf(895,plain,
! [B: $i,A: $i] :
( ( c_div @ ( c_uminus @ A @ tc_IntDef_Oint ) @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= ( c_div @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(254,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(1344,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
thf(1460,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
thf(943,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(231,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_NatArith_Oof__nat @ c_0 @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
thf(1293,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_NatArith_Oof__nat @ c_0 @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(485,axiom,
class_LOrder_Omeet__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(1820,plain,
class_LOrder_Omeet__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(697,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(2261,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(1821,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
thf(1731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
thf(799,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_minus @ ( c_insert @ B @ c_emptyset @ A ) @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(173,axiom,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) )
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
thf(1162,plain,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) )
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(179,axiom,
( ( c_uminus @ ( c_IntDef_Oint @ c_0 ) @ tc_IntDef_Oint )
= ( c_IntDef_Oint @ c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
thf(1177,plain,
( ( c_uminus @ ( c_IntDef_Oint @ c_0 ) @ tc_IntDef_Oint )
= ( c_IntDef_Oint @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
thf(1381,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(74,axiom,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(932,plain,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(549,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_0 != c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).
thf(1952,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_0 != c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
thf(1112,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(424,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
thf(1688,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(96,axiom,
! [A: $i] :
( ( c_div @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
thf(983,plain,
! [A: $i] :
( ( c_div @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(196,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
thf(1213,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(614,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Opprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
thf(2086,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Opprt @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(6,axiom,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(780,plain,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
thf(883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(690,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_in @ c_0 @ c_IntDef_OInts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
thf(2244,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_in @ c_0 @ c_IntDef_OInts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(319,axiom,
! [A: $i] :
( ( class_HOL_Otimes @ ( tc_set @ A ) )
| ~ ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_6) ).
thf(1477,plain,
! [A: $i] :
( ( class_HOL_Otimes @ ( tc_set @ A ) )
| ~ ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(751,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(2390,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(330,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_15) ).
thf(1496,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(649,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(2156,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(674,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs @ c_1 @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
thf(2207,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs @ c_1 @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(558,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ c_1 @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
thf(1973,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ c_1 @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(604,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
thf(2069,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_1 @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_1 @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(1396,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(771,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ B @ c_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
thf(2439,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ B @ c_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(537,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(1926,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(741,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(2365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
thf(1594,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(429,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(1699,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
thf(2212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
thf(959,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(656,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
thf(2171,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
thf(1445,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(44,axiom,
! [A: $i] :
( ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
thf(868,plain,
! [A: $i] :
( ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(1413,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(597,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
thf(2054,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(688,axiom,
! [B: $i,A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= ( c_times @ B @ c_0 @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(2239,plain,
! [B: $i,A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= ( c_times @ B @ c_0 @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( A = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( A = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(480,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( B = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
thf(1809,plain,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( B = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
thf(2096,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_IntDef_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_IntDef_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(314,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(1467,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ ( c_Suc @ B ) @ A )
= ( c_plus @ ( c_NatArith_Oof__nat @ B @ A ) @ c_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
thf(1081,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ ( c_Suc @ B ) @ A )
= ( c_plus @ ( c_NatArith_Oof__nat @ B @ A ) @ c_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(252,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(1340,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
thf(1551,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(702,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
thf(2271,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
= ( c_div @ B @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
thf(1905,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
= ( c_div @ B @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(291,axiom,
! [A: $i] :
( ~ ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat )
| ( c_less @ c_1 @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
thf(1420,plain,
! [A: $i] :
( ~ ( c_less @ ( c_Suc @ c_0 ) @ ( c_IntDef_Onat @ A ) @ tc_nat )
| ( c_less @ c_1 @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(225,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(1277,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(633,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
thf(2234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(812,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
thf(1509,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(565,axiom,
class_LOrder_Olorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(1990,plain,
class_LOrder_Olorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(671,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
thf(2202,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(727,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ c_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
thf(2333,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ c_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_0
!= ( c_NatArith_Oof__nat @ B @ A ) )
| ( c_0 = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_0
!= ( c_NatArith_Oof__nat @ B @ A ) )
| ( c_0 = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
thf(1181,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
thf(823,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(497,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
thf(1845,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(475,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
thf(1798,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(463,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
thf(1770,plain,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
= ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ ( tc_set @ C ) )
= ( c_minus @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(745,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ~ ( c_in @ C @ c_IntDef_OInts @ A )
| ( c_in @ ( c_times @ C @ B @ A ) @ c_IntDef_OInts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
thf(2375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_in @ B @ c_IntDef_OInts @ A )
| ~ ( c_in @ C @ c_IntDef_OInts @ A )
| ( c_in @ ( c_times @ C @ B @ A ) @ c_IntDef_OInts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(666,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(2192,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(2143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(406,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_6) ).
thf(1647,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(658,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(2175,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(758,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_times @ B @ C @ A )
!= c_0 )
| ( C = c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
thf(2407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_times @ B @ C @ A )
!= c_0 )
| ( C = c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(356,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
thf(1547,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ A @ B ) @ t_c ) @ ( c_times @ v_x @ ( v_h @ A @ B ) @ t_c ) @ t_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(776,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ A @ B ) @ t_c ) @ ( c_times @ v_x @ ( v_h @ A @ B ) @ t_c ) @ t_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(754,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
thf(2397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(113,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(1025,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(451,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(1743,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(282,axiom,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(1400,plain,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
thf(1230,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
thf(1484,plain,
! [B: $i,A: $i] :
( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(651,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
thf(2160,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(126,axiom,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1053,plain,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
thf(1716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(306,axiom,
! [A: $i] :
~ ( c_IntDef_Oneg @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
thf(1452,plain,
! [A: $i] :
~ ( c_IntDef_Oneg @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(184,axiom,
! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(1186,plain,
! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
thf(1901,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(352,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
thf(1538,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ A @ c_emptyset @ C ) @ ( tc_set @ C ) ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ A @ c_emptyset @ C ) @ ( tc_set @ C ) ) @ C )
= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(907,plain,
! [B: $i,A: $i] :
( ( c_minus @ c_emptyset @ A @ ( tc_set @ B ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
thf(1432,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(653,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
thf(2165,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(704,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(2276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(679,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
thf(2219,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(635,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(2128,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
thf(1934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(499,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
thf(1849,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(626,axiom,
class_LOrder_Ojoin__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(2113,plain,
class_LOrder_Ojoin__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(747,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_HOL_Oabs @ B @ A )
= ( c_uminus @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(2379,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_HOL_Oabs @ B @ A )
= ( c_uminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(722,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(2320,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(454,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
thf(1749,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Suc @ B ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
thf(1008,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Suc @ B ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(48,axiom,
! [A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
thf(876,plain,
! [A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_IntDef_Oint )
| ( ( c_IntDef_Onat @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
thf(859,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_IntDef_Oint )
| ( ( c_IntDef_Onat @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(598,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
thf(2056,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
!= c_emptyset )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(1358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_minus @ A @ B @ ( tc_set @ C ) )
!= c_emptyset )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(765,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
thf(2426,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(351,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
thf(1536,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(260,axiom,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(1353,plain,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(705,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
thf(2279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(738,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ C @ B @ tc_nat ) )
| ( A = C )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(2357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ C @ B @ tc_nat ) )
| ( A = C )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(550,axiom,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
thf(1955,plain,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(643,axiom,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(2145,plain,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(1094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(1140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(544,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
thf(1940,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(577,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
thf(2013,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(555,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(1966,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ C @ A ) @ B @ A )
= ( c_Nat_Opower @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
thf(1685,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ~ ( c_Parity_Oeven @ B @ tc_nat )
| ( ( c_Nat_Opower @ ( c_uminus @ C @ A ) @ B @ A )
= ( c_Nat_Opower @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(359,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(1553,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(60,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
thf(903,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(667,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(2194,plain,
class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(724,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_in @ B @ C @ A )
| ( c_lessequals @ ( c_SetsAndFunctions_Oelt__set__times @ B @ D @ A ) @ ( c_times @ C @ D @ ( tc_set @ A ) ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono3_0) ).
thf(2325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Otimes @ A )
| ~ ( c_in @ B @ C @ A )
| ( c_lessequals @ ( c_SetsAndFunctions_Oelt__set__times @ B @ D @ A ) @ ( c_times @ C @ D @ ( tc_set @ A ) ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(2226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(570,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ A ) @ B @ A ) @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
thf(1998,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ A ) @ B @ A ) @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
thf(1918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(407,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(1649,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(139,axiom,
( ( c_IntDef_Oint @ c_0 )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
thf(1084,plain,
( ( c_IntDef_Oint @ c_0 )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(171,axiom,
! [A: $i] :
( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
thf(1157,plain,
! [A: $i] :
( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(530,axiom,
class_LOrder_Olorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(1913,plain,
class_LOrder_Olorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(468,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
thf(1781,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
thf(891,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(664,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(186,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(1189,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(716,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(2305,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(730,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(2342,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_times @ B @ C @ tc_IntDef_Oint ) @ A )
= ( c_times @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
thf(1575,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_times @ B @ C @ tc_IntDef_Oint ) @ A )
= ( c_times @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
thf(1866,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(605,axiom,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(2071,plain,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(224,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(1276,plain,
class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(773,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(2443,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(247,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(1326,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
thf(1253,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_div @ ( c_plus @ B @ A @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint )
= ( c_plus @ ( c_div @ B @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(275,axiom,
! [A: $i] :
( ( c_div @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_div @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
thf(1385,plain,
! [A: $i] :
( ( c_div @ ( c_Suc @ c_0 ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_div @ c_1 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(654,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
thf(2167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanLessThan @ C @ D @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(707,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
thf(2283,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( ( c_LOrder_Omeet @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( ( c_LOrder_Omeet @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(418,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
thf(1674,plain,
c_0 != c_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(321,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(1481,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(452,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
thf(1745,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(501,axiom,
class_Orderings_Oord @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(1854,plain,
class_Orderings_Oord @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(636,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
thf(2130,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(761,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
thf(2416,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
thf(995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(753,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(2394,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(710,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( ( c_times @ c_0 @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
thf(2290,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( ( c_times @ c_0 @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(693,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
thf(2251,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(573,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
thf(2004,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(575,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(2009,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(327,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(1491,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(755,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( ( c_times @ B @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
thf(2399,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( ( c_times @ B @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(433,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
thf(1706,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(662,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
thf(2183,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(413,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
thf(1661,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(631,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_1 @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
thf(2120,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_1 @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(763,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ B @ C @ A )
!= ( c_times @ B @ D @ A ) )
| ( C = D )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).
thf(2421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_times @ B @ C @ A )
!= ( c_times @ B @ D @ A ) )
| ( C = D )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(726,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
!= ( c_HOL_Oabs @ B @ A ) )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
thf(2330,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
!= ( c_HOL_Oabs @ B @ A ) )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
thf(1077,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(740,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(652,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_1 != c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__neq__zero_0) ).
thf(2162,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_1 != c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(618,axiom,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(2095,plain,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ A )
= ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ A )
= ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(684,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(2230,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(589,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
thf(2036,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(239,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(1309,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
thf(1908,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(696,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
thf(2258,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(257,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1348,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
thf(1512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(715,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ c_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
thf(2302,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ c_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(443,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
thf(1725,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(749,axiom,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(2385,plain,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(685,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(2233,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(1625,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
thf(1303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
thf(1757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
thf(999,plain,
! [B: $i,A: $i] :
( ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_IntDef_Onat @ ( c_Divides_Oop_Amod @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
thf(2287,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(404,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_0 @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
thf(1642,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_0 @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(621,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(2102,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(370,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_in @ c_1 @ c_IntDef_OInts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
thf(1578,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_in @ c_1 @ c_IntDef_OInts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(1957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(648,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(2155,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(695,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
thf(2255,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_plus @ A @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(835,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(346,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
thf(1527,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(167,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
thf(1148,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
= ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
thf(790,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
= ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ ( c_times @ B @ C @ tc_nat ) @ A )
= ( c_times @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
thf(1436,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( ( c_NatArith_Oof__nat @ ( c_times @ B @ C @ tc_nat ) @ A )
= ( c_times @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(67,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(918,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(241,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(1314,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(483,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
thf(1816,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_1 @ B @ tc_nat )
| ( c_less @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_1 @ B @ tc_nat )
| ( c_less @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(426,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(1693,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ~ ( c_less @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
| ( c_less @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
thf(1789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ B @ A )
| ~ ( c_less @ ( c_Nat_Opower @ B @ C @ A ) @ ( c_Nat_Opower @ B @ D @ A ) @ A )
| ( c_less @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(26,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(828,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_div @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(591,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_0
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
thf(2040,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_0
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
thf(955,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_div @ A @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
thf(886,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_div @ A @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(1710,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(190,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(1197,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(616,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
thf(2091,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(757,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= C )
| ( C = c_0 )
| ( B = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
thf(2404,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= C )
| ( C = c_0 )
| ( B = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(681,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
= ( c_HOL_Oabs @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
thf(2223,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
= ( c_HOL_Oabs @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(256,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
thf(1346,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ ( c_IntDef_Oint @ ( c_Numeral_Onumber__of @ A @ tc_nat ) ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(601,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_0) ).
thf(2063,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(388,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
thf(1610,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
!= ( c_IntDef_Oint @ B ) )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
!= ( c_IntDef_Oint @ B ) )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(767,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
thf(2430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(349,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).
thf(1532,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(1976,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(100,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_0
= ( c_NatArith_Oof__nat @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).
thf(992,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_0
= ( c_NatArith_Oof__nat @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ C @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ C @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(36,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
thf(850,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(234,axiom,
! [A: $i] :
( ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) )
= ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_2) ).
thf(1299,plain,
! [A: $i] :
( ~ ( c_lessequals @ c_0 @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) )
= ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_IntDef_Onat @ A ) @ ( c_IntDef_Onat @ B ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(744,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(2372,plain,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(640,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
thf(2138,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(539,axiom,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(1930,plain,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(736,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(2353,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
thf(1236,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_0 @ ( c_NatArith_Oof__nat @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
!= ( c_IntDef_Oof__int @ B @ A ) )
| ( c_0 = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
thf(2241,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
!= ( c_IntDef_Oof__int @ B @ A ) )
| ( c_0 = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_minus @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) )
= ( c_minus @ D @ B @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_minus @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) )
= ( c_minus @ D @ B @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(372,axiom,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(1582,plain,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(699,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(2265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(381,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
thf(1597,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
thf(1880,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_IntDef_Oint @ B ) @ A )
= ( c_NatArith_Oof__nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_IntDef_Oint @ B ) @ A )
= ( c_NatArith_Oof__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(553,axiom,
( ( c_times @ c_1 @ c_1 @ tc_nat )
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
thf(1962,plain,
( ( c_times @ c_1 @ c_1 @ tc_nat )
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(580,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(2018,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ( c_lessequals @ ( c_NatArith_Oof__nat @ B @ A ) @ ( c_NatArith_Oof__nat @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(735,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(2351,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
thf(1812,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(2106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
thf(1870,plain,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
thf(1331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(386,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(1606,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(546,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_1 @ B @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
thf(1944,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_1 @ B @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ A @ ( c_plus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
thf(1367,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_minus @ A @ ( c_plus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_plus @ B @ C @ tc_IntDef_Oint ) @ A )
= ( c_plus @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
thf(940,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_IntDef_Oof__int @ ( c_plus @ B @ C @ tc_IntDef_Oint ) @ A )
= ( c_plus @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(70,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oordered__semidom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
thf(923,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oordered__semidom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(421,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
thf(1681,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(607,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( c_in @ c_1 @ c_IntDef_ONats @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
thf(2074,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( c_in @ c_1 @ c_IntDef_ONats @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(312,axiom,
c_lessequals @ ( c_IntDef_Oint @ c_0 ) @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
thf(1463,plain,
c_lessequals @ ( c_IntDef_Oint @ c_0 ) @ c_0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(326,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(1490,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(119,axiom,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
thf(1037,plain,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(713,axiom,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(2297,plain,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( v_h @ A @ B ) @ t_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(775,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( v_h @ A @ B ) @ t_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2445,plain,
$false,
inference(e,[status(thm)],[2199,1411,1469,2295,1729,846,1899,1315,962,1179,777,1586,809,1337,1718,1369,1823,1190,2336,2109,1454,2031,2072,1767,1995,2263,909,1031,893,1840,1818,1295,1950,1549,2309,1068,1522,1618,1073,1544,1793,1305,1041,1855,2077,1924,1005,2210,2117,1596,1290,1882,1443,1808,1422,1939,873,1205,2099,1591,2114,1142,1269,1426,1608,1655,1137,1735,2184,814,1260,1988,913,1640,945,1063,2146,1458,2195,1705,1164,797,2434,1872,1507,1222,2360,829,1835,2216,2348,2046,1391,1613,1601,2082,2173,1529,1887,2432,1914,1243,1127,782,1441,2020,841,973,885,1046,1650,1645,1724,1475,2136,1904,1703,1228,1623,1628,1055,1287,1430,1985,1760,2339,2269,1860,1323,2274,802,1826,1279,1455,934,2126,1132,949,2049,870,1479,1013,2158,1773,1494,1362,1232,1847,1922,817,1892,1379,2169,1514,969,1572,1741,1398,881,1931,1568,1875,1778,2007,1302,1450,1373,1334,1828,1383,1183,821,1714,2027,1109,1632,1418,2236,1858,1864,2122,1151,937,1677,2034,2017,905,1169,1377,2281,1215,1447,1394,1351,2002,1345,2392,2205,1843,2058,2367,2437,1928,1896,2190,866,1886,1119,1622,2424,774,2103,1405,1104,1697,1604,2011,2204,1691,793,925,1199,1153,2307,1057,1708,2093,1868,2382,2061,1636,1274,957,2428,952,1217,1666,1487,2132,1560,1387,1723,2249,1021,778,1355,1580,1123,862,1570,1174,1502,1751,788,2150,1370,1238,2015,916,1365,1920,1457,2068,1210,1407,2344,1910,1837,1602,1968,879,852,1555,889,2179,1787,2181,1079,2327,1634,2228,1936,1592,1762,1851,2377,1534,1804,1970,1856,1672,1540,1878,1755,857,1089,1234,1375,1121,980,1498,1683,1329,1160,1361,2323,1739,1424,2080,1842,1791,2349,2038,1889,1028,2023,1964,1942,1659,2419,1075,1016,1207,1612,1039,970,2317,1155,837,1297,1530,911,1947,1984,1002,1720,1979,2140,1114,1324,2285,1776,1263,997,1588,1099,985,1266,2153,2387,1831,2355,1192,1060,1050,2052,1599,1627,2370,1525,1434,1202,1241,805,2043,1695,921,1712,2076,1035,1187,1026,1616,1996,1991,1318,1814,1086,1071,2402,1663,2089,1515,2221,953,1185,1135,2001,1727,2176,1959,1219,1483,1747,1251,2413,1146,1754,2253,2033,819,975,1833,1916,2048,1884,1652,1403,1520,2134,1784,1389,843,1125,875,826,1795,1701,1256,1226,1488,1428,1503,1669,2029,2293,1271,1312,1107,2442,1092,1258,2148,1765,1090,1897,919,1464,947,1638,1224,2119,900,831,1408,1282,1894,1524,1048,1349,1542,1144,2116,1771,1439,2065,1194,2346,2079,2311,2084,2214,784,1117,1574,1806,1011,1589,990,2246,1492,2299,1043,1801,2197,1307,1471,2025,1557,2314,2111,1993,2267,1862,848,2410,895,964,1344,1460,943,1293,1820,2261,1821,1731,799,1162,1177,1381,932,1952,1112,1688,983,1213,1245,2086,780,883,2244,1477,2390,1496,1102,2156,2207,1973,2069,1562,1396,2439,1926,2365,1594,1699,2212,959,2171,1445,868,1413,2054,2239,1583,1809,2096,1166,1467,927,1081,1340,1551,795,2271,1905,1420,1277,2124,2234,812,1509,1990,2202,2333,1018,1181,823,1845,1798,1770,855,2375,2192,2143,1647,2175,2407,1547,776,2397,1025,1743,1400,1230,1484,2160,1053,1716,1452,1186,1901,1538,1679,1285,1220,907,1432,2165,2276,2219,2128,1934,1849,2113,1023,2379,2320,864,1749,1008,876,859,2056,1358,2426,1536,1981,1353,2279,2357,1955,2145,1094,978,1140,1940,2013,1966,1685,1553,903,2194,1517,2325,2226,1998,1918,1649,1084,1157,1913,1781,891,2187,1189,2305,2342,1575,1866,2071,1276,2443,1326,1253,1385,2167,2283,1341,1674,1481,1745,1854,2130,786,2416,995,2394,2290,2251,1629,2004,2009,1491,2399,1706,2183,1661,2120,2421,929,2330,1077,2362,2162,2095,832,2230,2036,1309,1908,2258,1348,1512,2302,1725,2385,967,2233,1625,1303,1757,999,2287,1642,2102,1578,1957,2155,2255,1097,835,1527,1148,1248,790,1436,918,1314,1816,1657,1693,1789,828,1065,2040,955,886,1172,897,1033,1710,1197,2091,2404,2223,1473,1346,2063,1610,1129,2430,1532,1976,992,1500,850,1299,1505,2372,2138,1930,2353,1236,2241,987,1582,2265,1597,1880,1320,1962,2018,1416,2351,1812,2106,1870,1331,1606,1944,1367,940,923,1737,1681,2074,1463,1565,1490,1037,2297,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA042-1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 17:44:54 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.14/1.19 % [INFO] Parsing done (325ms).
% 2.14/1.20 % [INFO] Running in sequential loop mode.
% 2.65/1.41 % [INFO] eprover registered as external prover.
% 2.65/1.41 % [INFO] cvc4 registered as external prover.
% 2.65/1.42 % [INFO] Scanning for conjecture ...
% 3.26/1.57 % [INFO] Found a conjecture and 2782 axioms. Running axiom selection ...
% 4.44/1.85 % [INFO] Axiom selection finished. Selected 768 axioms (removed 2014 axioms).
% 4.98/1.99 % [INFO] Problem is propositional (TPTP CNF).
% 4.98/2.00 % [INFO] Type checking passed.
% 4.98/2.01 % [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 ...
% 10.82/3.49 % External prover 'e' found a proof!
% 10.82/3.49 % [INFO] Killing All external provers ...
% 10.82/3.49 % Time passed: 2979ms (effective reasoning time: 2282ms)
% 10.82/3.49 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.82/3.49 % Axioms used in derivation (768): cls_IntDef_Ozero__less__int__conv_0, cls_Nat_Onot__gr0_0, cls_IntDiv_Ozdiv__zadd__self1_0, cls_OrderedGroup_Ojoin__0__eq__0_1, cls_Divides_Odiv__mult__self1_0, cls_Set_OPow__UNIV_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Power_Opower__0__Suc_0, cls_Set_OPow__iff_1, cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, cls_Parity_Opower__less__zero__eq__number__of_0, clsrel_Ring__and__Field_Opordered__comm__semiring_14, cls_Parity_Opower__le__zero__eq__number__of_1, clsrel_Ring__and__Field_Opordered__semiring_3, cls_Nat_Onot__less0_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_Nat_Oone__eq__mult__iff_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6, cls_NatArith_Oadd__diff__assoc2_0, cls_SetInterval_OgreaterThanLessThan__iff_0, cls_NatArith_Oof__nat__0__le__iff_0, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_Power_Onat__zero__less__power__iff_2, cls_SetInterval_OgreaterThanAtMost__iff_2, cls_Set_Osingleton__insert__inj__eq_0, cls_Parity_Oeven__nat__power_2, cls_IntDef_Ozless__int_0, cls_SetInterval_OatMost__0_0, clsarity_nat_32, cls_IntDef_Oint__eq__0__conv_1, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17, cls_Parity_Oeven__sum_2, cls_Set_OUNIV__not__empty_0, cls_Set_OsubsetI_1, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Nat_Onat__add__left__cancel__less_1, clsrel_Ring__and__Field_Oordered__semidom_16, cls_IntDef_Ozless__nat__conj_1, cls_NatBin_Opower__nat__number__of__number__of_1, cls_Parity_Opower__eq__0__iff__number__of_2, cls_Divides_Omod__eq__0D__dest_0, cls_IntDiv_Ozmod__self_0, cls_Nat_Onat__add__right__cancel_0, cls_Parity_Ozero__less__power__eq__number__of_4, cls_IntDef_Oof__int__0__le__iff_0, clsarity_IntDef__Oint_46, cls_IntDiv_Ozmod__zmult__self1_0, cls_Parity_Oeven__difference_2, cls_IntDef_Oof__int__0__less__iff_0, cls_Nat_Oop_A_K_Omult__Suc_0, clsarity_IntDef__Oint_52, clsarity_IntDef__Oint_24, cls_Parity_Oeven__nat__product_2, cls_NatArith_Oof__nat__mult_0, clsrel_OrderedGroup_Olordered__ab__group_9, clsrel_Ring__and__Field_Oordered__ring__strict_26, cls_IntDiv_Ozdiv__1_0, cls_IntDef_Oint__nat__eq_0, clsrel_Ring__and__Field_Oordered__semidom_39, cls_Set_ODiff__cancel_0, clsrel_Ring__and__Field_Oordered__idom_12, cls_Set_Osubset__UNIV_0, clsrel_Ring__and__Field_Ofield_8, cls_Set_Oinsert__Diff1_0, cls_Nat_Omult__le__cancel1_1, cls_Parity_Oeven__nat__product_1, clsrel_OrderedGroup_Omonoid__mult_2, cls_NatArith_Oof__nat__0__eq__iff_1, cls_Nat_Oless__one_1, clsrel_Power_Orecpower_21, clsrel_Ring__and__Field_Oordered__semidom_28, cls_Nat_Odiff__is__0__eq_0, cls_OrderedGroup_Opprt__eq__id_0, cls_Parity_Oeven__nat__sum_1, cls_Finite__Set_OFinites_OemptyI_0, cls_IntDef_Oof__int__of__nat__eq_0, cls_Nat_OSuc__Suc__eq_0, clsarity_nat_40, cls_NatArith_Oof__nat__add_0, cls_Nat_Oop_A_K_Omult__0_0, cls_Power_Ozero__less__power__abs__iff_2, cls_IntDiv_Ozdiv__zminus__zminus_0, clsrel_Ring__and__Field_Ofield_32, clsrel_Ring__and__Field_Ofield_5, cls_Orderings_Oorder__less__irrefl_0, cls_Parity_Ozero__less__power__eq__number__of_1, cls_IntDef_Oint__Suc_0, cls_IntDiv_Ozero__less__zpower__abs__iff_2, cls_OrderedGroup_Oabs__ge__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_NatArith_Oof__nat__less__iff_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, cls_SetInterval_OatLeast__iff_1, cls_Set_Osingleton__inject__dest_0, clsrel_OrderedGroup_Olordered__ab__group__abs_18, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_Finite__Set_OFinites_OinsertI_0, cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, cls_Nat_Odiff__0__eq__0_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_IntDef_Oneg__zminus__int_0, cls_Divides_Odiv__less_0, cls_Divides_Odiv__1_0, cls_NatBin_Oint__nat__number__of_1, cls_Set_OCompl__iff_1, cls_IntDef_Onegative__eq__positive_0, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__0__eq_0, cls_IntDef_OInts__0_0, clsarity_IntDef__Oint_56, cls_Parity_Opower__minus__even_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_IntDef_Oint__less__0__conv_0, cls_OrderedGroup_Onprt__mono_0, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, clsarity_set_2, cls_IntDiv_ODIVISION__BY__ZERO_0, clsarity_nat_3, clsrel_Power_Orecpower_24, clsarity_IntDef__Oint_3, cls_NatBin_Oeq__0__number__of_1, cls_NatArith_Oof__nat__less__0__iff_0, cls_Ring__and__Field_Omult__cancel__left1_2, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Onat__le__0_0, cls_SetInterval_OatMost__iff_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Nat_Ozero__less__diff_1, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_IntDiv_Ozmod__zmult__self2_0, clsrel_Ring__and__Field_Ocomm__ring__1_7, cls_OrderedGroup_Oneg__meet__eq__join_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_IntDef_Ozero__less__int__conv_1, cls_NatBin_OSuc__nat__number__of_0, cls_Numeral_Obin__rel__simps__9_0, cls_Power_Opower_Osimps__2_0, cls_Divides_Omod__add__self1_0, cls_Parity_Opower__0__left__number__of_1, clsrel_OrderedGroup_Olordered__ab__group__meet_9, cls_Power_Opower__one__right_0, cls_Set_OPow__iff_0, cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0, cls_SetsAndFunctions_Oset__times__intro2_0, cls_IntDef_Oof__int__less__iff_0, clsarity_nat_29, clsrel_Ring__and__Field_Ocomm__ring__1_24, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_Nat_Omult__less__cancel2_1, cls_IntDef_OInts__add_0, cls_NatArith_Odiff__diff__right_0, cls_IntDiv_Omod__div__trivial_0, cls_Power_Opower__eq__0__iff_2, clsarity_IntDef__Oint_0, cls_Ring__and__Field_Ofield__mult__cancel__left_1, cls_SetsAndFunctions_Oset__times__mono2_0, cls_Set_OpsubsetI_0, cls_Set_Osubset__refl_0, cls_IntDef_Oof__nat__in__Nats_0, cls_Divides_Odiv__mult__self__is__m_0, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1, cls_Set_ODiff__UNIV_0, cls_Parity_Oeven__power_2, cls_Nat_Omult__0__right_0, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Set_OCompl__eq__Compl__iff_0, cls_LOrder_Ojoin__idempotent_0, cls_Nat_Onat__add__left__cancel__le_0, cls_Ring__and__Field_Omult__cancel__right1_2, cls_Divides_Odiv__less__dividend_0, cls_List_Ochar_Oinject_0, cls_NatBin_Odiv__nat__number__of_0, cls_Nat_Omult__less__cancel1_1, cls_Nat_Omult__eq__1__iff_0, cls_IntDef_Onot__neg__int_0, cls_Nat_Oadd__gr__0_2, clsrel_OrderedGroup_Olordered__ab__group__abs_0, cls_Nat_Onat__add__left__cancel__less_0, cls_Finite__Set_Ofinite__Diff__insert_1, cls_NatBin_Odiv__nat__number__of_1, cls_SetInterval_Ofinite__greaterThanAtMost_0, cls_SetInterval_OatLeastLessThan__iff_2, cls_NatArith_Oof__nat__le__iff_0, clsrel_Ring__and__Field_Ofield_17, cls_Power_Opower__strict__increasing__iff_0, cls_Power_Ozero__le__power__abs_0, cls_OrderedGroup_Omeet__0__eq__0_0, cls_Set_ODiff__iff_2, cls_OrderedGroup_Oabs__eq__0_0, clsarity_nat_36, cls_IntDef_Ozero__less__nat__eq_1, cls_IntArith_Oint__eq__iff__number__of_1, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, cls_SetInterval_OatLeastAtMost__empty_0, cls_Power_Opower__increasing__iff_1, cls_Nat_Omult__eq__1__iff_2, cls_Nat_Omult__le__cancel1_0, cls_IntDef_Oof__int__le__0__iff_1, cls_Nat_Oless__one_0, cls_IntDiv_Omod__mod__trivial_0, cls_Nat_Odiff__Suc__Suc_0, cls_IntDef_Oof__int__minus_0, clsrel_Ring__and__Field_Oordered__semidom_35, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, cls_IntDef_Oint__nat__eq_1, clsarity_IntDef__Oint_48, clsrel_OrderedGroup_Ocomm__monoid__mult_3, cls_SetInterval_OatLeastAtMost__iff_2, cls_Set_Osubset__empty_0, cls_Parity_Oeven__neg_0, clsrel_OrderedGroup_Olordered__ab__group_6, cls_SetsAndFunctions_Oset__times__intro_0, cls_Nat_Ole__add__diff__inverse2_0, cls_Parity_Ozero__less__power__nat__eq__number__of_1, clsarity_IntDef__Oint_58, cls_Set_OsubsetI_0, cls_Divides_Omod__le__divisor_0, clsrel_Ring__and__Field_Oordered__idom_38, cls_Nat_Omult__less__cancel2_0, cls_IntDiv_Opower_Osimps__2_0, cls_Parity_Oeven__nat__power_0, clsarity_nat_11, cls_Parity_Ozero__less__power__nat__eq__number__of_0, cls_NatArith_Oof__nat_Oof__nat__Suc_0, clsrel_Ring__and__Field_Oordered__idom_51, cls_Power_Onat__one__le__power_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_Set_OUNIV__I_0, cls_SetInterval_OatLeastAtMost__singleton_0, clsarity_set_6, cls_Set_ODiff__insert0_0, cls_Parity_Ozero__le__power__eq__number__of_1, cls_IntDef_Onegative__eq__positive_2, cls_Parity_Opower__le__zero__eq__number__of_5, clsrel_Ring__and__Field_Osemiring__0__cancel_3, clsrel_Power_Orecpower_7, clsrel_Ring__and__Field_Oordered__idom_52, cls_Infinite__Set_Onat__infinite_0, clsrel_Ring__and__Field_Oordered__idom_36, cls_Divides_Omod__mult__self1_0, clsrel_Ring__and__Field_Oordered__idom_42, cls_Set_Oinsert__subset_2, cls_Power_Ozero__less__power__abs__iff_0, cls_OrderedGroup_Ozero__le__pprt_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, clsrel_Ring__and__Field_Oordered__ring__strict_27, cls_Nat_Oadd__is__0_1, cls_Parity_Oeven__sum_0, clsrel_Ring__and__Field_Opordered__comm__semiring_13, cls_Parity_Opower__eq__0__iff__number__of_1, cls_Parity_Oeven__nat__power_1, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Parity_Oeven__product_0, cls_OrderedGroup_Ojoin__0__eq__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_Power_Orecpower__class_Oaxioms__1_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0, cls_Ring__and__Field_Onot__one__le__zero_0, cls_IntDef_Oof__int__less__iff_1, cls_NatArith_Oof__nat__le__0__iff_1, clsrel_Ring__and__Field_Oordered__idom_47, cls_IntDef_Oof__int__0__le__iff_1, cls_NatArith_Oof__nat__0__less__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_36, cls_SetInterval_OatLeast__subset__iff_0, cls_Finite__Set_Ofinite__insert_0, cls_NatArith_Oof__nat__1_0, cls_Set_Oinsert__iff_2, cls_Parity_Oeven__difference_1, cls_Parity_Opower__le__zero__eq__number__of_0, clsrel_OrderedGroup_Olordered__ab__group_17, cls_Power_Ozero__less__power__abs__iff_1, cls_Set_OCompl__subset__Compl__iff_0, cls_Nat_Omult__le__cancel2_2, clsrel_Ring__and__Field_Ocomm__ring__1_21, cls_Nat_Omult__cancel1_1, cls_OrderedGroup_Onprt__le__zero_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, cls_Nat_Onat__0__less__mult__iff_0, cls_Divides_Onat__mod__div__trivial_0, cls_IntDiv_Ozero__less__zpower__abs__iff_1, cls_IntDef_Oof__int__eq__iff_0, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_NatArith_Oof__nat__le__0__iff_0, clsrel_Ring__and__Field_Oordered__idom_18, cls_Set_Oinsert__not__empty_0, cls_Divides_Odiv__mult__self1__is__m_0, cls_NatBin_Omod__nat__number__of_1, cls_SetInterval_OgreaterThan__iff_0, cls_Set_OsingletonD__dest_0, cls_IntDef_Oof__int__0__eq__iff_0, cls_Divides_Odiv__mult__mult2_0, cls_Nat_Ole__0__eq_0, cls_Power_Opower__inject__exp_0, cls_SetInterval_Osingle__Diff__lessThan_0, clsrel_Ring__and__Field_Oordered__ring__strict_16, cls_Ring__and__Field_Omult__cancel__right1_1, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_NatArith_Odiff__less_0, cls_Divides_ODIVISION__BY__ZERO__DIV_0, clsrel_Ring__and__Field_Oordered__idom_22, cls_SetInterval_OlessThan__iff_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_Nat_Ozero__less__diff_0, cls_Set_Oempty__subsetI_0, cls_Divides_Omod__add__self2_0, clsarity_IntDef__Oint_31, cls_Parity_Oeven__nat__sum_0, cls_Power_Opower_Osimps__1_0, cls_Power_Opower__eq__0__iff_0, cls_Nat_OSuc__le__mono_0, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_SetInterval_Ofinite__lessThan_0, cls_Ring__and__Field_Omult__cancel__left1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_6, cls_IntDef_Oabs__int__eq_0, cls_Parity_Oeven__sum_3, cls_SetsAndFunctions_Oset__times__mono4_0, cls_Parity_Ozero__less__power__eq__number__of_3, cls_List_Odrop__0_0, cls_Ring__and__Field_Omult__eq__0__iff_0, cls_IntDiv_Ozdiv__zero_0, cls_IntDiv_Opos__mod__sign_0, cls_Nat_Oone__le__mult__iff_1, clsrel_Ring__and__Field_Oordered__idom_11, cls_Nat_OSuc__less__eq_1, clsrel_OrderedGroup_Olordered__ab__group__meet_17, cls_Parity_Opower__le__zero__eq__number__of_4, cls_Set_Oempty__iff_0, cls_Set_OsubsetD_0, cls_IntDef_OInts__1_0, clsarity_nat_37, cls_IntDef_OInts__diff_0, cls_SetInterval_OatLeastLessThan__iff_1, cls_IntDef_ONats__0_0, cls_Set_OsingletonI_0, cls_Set_OCompl__empty__eq_0, cls_Set_ODiff__iff_1, cls_IntDef_Oint__int__eq_0, clsrel_LOrder_Olorder_0, cls_Divides_Omod__mult__self1__is__0_0, cls_SetInterval_OatLeastLessThan__iff_0, cls_Parity_Opower__0__left__number__of_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Set_Oempty__Diff_0, clsrel_Ring__and__Field_Ofield_0, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, clsrel_Ring__and__Field_Oaxclass__abs__if_1, cls_Parity_Oeven__nat__zero_0, clsrel_Ring__and__Field_Ocomm__ring__1_8, cls_Divides_Omod__less__divisor_0, cls_Nat_Omult__cancel2_0, clsarity_set_14, cls_Nat_Omult__less__cancel1_0, cls_Ring__and__Field_Ozero__le__one_0, cls_Set_Osubset__antisym_0, cls_Ring__and__Field_Omult__cancel__left2_0, cls_IntDef_Oof__int__add_0, cls_Parity_Oeven__power_1, clsarity_nat_6, cls_IntDef_Ozless__nat__conj_2, cls_NatBin_Oint__nat__number__of_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Finite__Set_Ofinite__Diff__insert_0, clsarity_IntDef__Oint_37, clsrel_Ring__and__Field_Oordered__semidom_12, cls_SetInterval_OatMost__iff_0, cls_Power_Opower__strict__increasing__iff_1, cls_IntDef_OInts__minus_0, clsarity_nat_43, clsrel_Orderings_Oorder_0, cls_IntDef_Onegative__eq__positive_1, cls_IntDef_Oof__int__1_0, cls_NatBin_Oeq__nat__number__of_10, cls_Set_OCompl__iff_0, cls_Divides_Omod__1_0, cls_Nat_Omult__cancel2_1, clsrel_OrderedGroup_Olordered__ab__group__abs_16, cls_Nat_Onat__0__less__mult__iff_1, clsrel_LOrder_Omeet__semilorder_0, cls_SetInterval_OgreaterThanLessThan__iff_2, clsrel_Power_Orecpower_3, clsarity_IntDef__Oint_29, cls_Set_Osubset__empty_1, cls_Finite__Set_Ofinite__Pow__iff_0, clsrel_Ring__and__Field_Oordered__idom_46, clsrel_Ring__and__Field_Oordered__semidom_38, clsrel_OrderedGroup_Olordered__ab__group__meet_15, cls_IntDiv_Ozmod__zero_0, cls_Set_Oall__not__in__conv_0, cls_Nat_OSuc__diff__diff_0, cls_OrderedGroup_Opprt__0_0, cls_IntArith_Oone__less__nat__eq_1, cls_Finite__Set_Oof__nat__id_0, cls_SetsAndFunctions_Oset__times__mono3_0, cls_NatBin_Omod__nat__number__of_2, clsarity_IntDef__Oint_18, cls_Set_Oinsert__iff_1, clsrel_OrderedGroup_Olordered__ab__group__join_8, cls_IntArith_Oint__eq__iff__number__of_0, cls_Set_Osingleton__insert__inj__eq_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsarity_nat_34, cls_Parity_Ozero__less__power__nat__eq__number__of_2, clsarity_nat_45, cls_IntDef_OInts__mult_0, cls_Nat_OSuc__le__mono_1, clsrel_Ring__and__Field_Oordered__ring__strict_35, cls_Infinite__Set_Oatmost__one__unique_0, clsarity_set_1, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1, cls_NatBin_Omult__nat__number__of_0, cls_OrderedGroup_Opprt__eq__0_0, cls_Set_Oinsert__subset_1, cls_IntDiv_Ozdiv__zmult__self1_0, cls_NatBin_Onat__number__of_0, cls_SetInterval_OatLeastLessThan__empty_0, cls_Set_Oinsert__Diff__single_0, cls_Divides_Omod__mult__self2_0, cls_OrderedGroup_Oabs__of__nonpos_0, cls_NatArith_Odiff__Suc__diff__eq2_0, cls_SetInterval_OatLeastAtMost__iff_1, clsarity_nat_17, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4, cls_IntDef_Oof__int__less__0__iff_0, cls_SetInterval_OgreaterThanAtMost__iff_0, clsrel_Ring__and__Field_Oordered__semidom_36, cls_IntArith_Ozle__add1__eq__le_1, cls_NatArith_Oof__nat__0__less__iff_0, cls_Parity_Oeven__nat__Suc_1, cls_NatBin_Oadd__nat__number__of_1, cls_OrderedGroup_Opprt__mono_0, cls_IntDef_Onat__int_0, cls_Ring__and__Field_Oright__inverse_0, cls_IntArith_Ozabs__less__one__iff_0, clsrel_LOrder_Ojoin__semilorder_1, cls_Nat_Odiff__is__0__eq_H_0, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_Ring__and__Field_Oordered__idom_35, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, cls_Nat_Oadd__gr__0_0, cls_Set_OCompl__UNIV__eq_0, clsarity_IntDef__Oint_54, clsrel_OrderedGroup_Olordered__ab__group__join_16, cls_NatBin_Oone__mod__nat__number__of_0, clsrel_Ring__and__Field_Ofield_6, cls_OrderedGroup_Oabs__minus__cancel_0, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Parity_Opower__le__zero__eq__number__of_3, cls_Nat_Oless__Suc0_0, cls_IntDef_Oint__1_0, clsrel_LOrder_Olorder_2, cls_NatArith_Oof__nat__eq__0__iff_0, cls_IntDef_Onot__zle__0__negative_0, cls_Nat_Oadd__is__0_2, cls_Nat_Oop_A_N_Odiff__0_0, cls_Parity_Opower__less__zero__eq__number__of_2, cls_OrderedGroup_Onprt__eq__0_0, cls_Parity_Oeven__difference_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_IntArith_Ozle__diff1__eq_0, cls_Nat_Onot__add__less1_0, cls_Parity_Oodd__one_0, cls_OrderedGroup_Ozero__less__abs__iff_1, cls_SetInterval_OatLeast__subset__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_24, cls_NatArith_Odiff__diff__cancel_0, cls_OrderedGroup_Oabs__eq__0_1, cls_SetInterval_OatLeastLessThan__singleton_0, cls_Ring__and__Field_Onot__one__less__zero_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, cls_Parity_Oeven__nat__sum_2, clsrel_OrderedGroup_Olordered__ab__group_15, cls_SetInterval_Ofinite__greaterThanLessThan_0, clsrel_Ring__and__Field_Oordered__idom_41, clsarity_IntDef__Oint_32, clsrel_Ring__and__Field_Oordered__ring__strict_28, cls_SetsAndFunctions_Oset__one__times_0, cls_Ring__and__Field_Omult__cancel__left1_0, cls_Parity_Oeven__product_1, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, clsrel_Ring__and__Field_Oordered__semidom_0, cls_NatBin_Omod__nat__number__of_0, clsrel_Ring__and__Field_Oordered__ring__strict_9, cls_IntDef_Onot__int__zless__negative_0, cls_Nat_Omult__cancel1_0, cls_Parity_Ozero__less__power__eq__number__of_2, cls_IntDiv_Ozmod__zadd__self2_0, cls_OrderedGroup_Oabs__le__zero__iff_0, cls_Parity_Oeven__power_0, clsrel_LOrder_Ojoin__semilorder_0, clsarity_IntDef__Oint_22, cls_IntDef_Oof__int__mult_0, clsarity_IntDef__Oint_5, cls_Nat_Omult__le__cancel2_1, cls_SetInterval_OlessThan__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_3, cls_Nat_Oone__eq__mult__iff_2, cls_Nat_Odiff__Suc__less_0, cls_Ring__and__Field_Omult__zero__right_0, clsarity_nat_5, cls_Ring__and__Field_Oone__neq__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_2, cls_Nat_OOne__nat__def_0, cls_IntDiv_Oneg__mod__bound_0, cls_Nat_Oadd__0__right_0, cls_Nat_Ole__add__diff__inverse_0, cls_Power_Onat__zero__less__power__iff_1, clsrel_LOrder_Olorder_1, cls_Set_Oempty__not__insert_0, clsrel_Ring__and__Field_Oordered__idom_8, cls_Nat_Onot__gr0_1, clsrel_Ring__and__Field_Oordered__semidom_11, cls_SetInterval_OgreaterThan__iff_1, cls_Nat_Onot__add__less2_0, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_Set_ODiff__eq__empty__iff_0, cls_Set_OpsubsetE_0, cls_IntDiv_Oneg__mod__sign_0, cls_Nat_Oadd__Suc__right_0, cls_IntDiv_Ozero__less__zpower__abs__iff_0, clsrel_Ring__and__Field_Opordered__comm__semiring_6, cls_NatArith_Oof__nat__eq__0__iff_1, clsarity_IntDef__Oint_43, cls_IntDef_ONats__add_0, cls_Set_ODiff__eq__empty__iff_1, clsrel_Ring__and__Field_Oordered__semidom_26, cls_IntDef_Ozless__int_1, cls_Set_ODiff__empty_0, clsrel_Ring__and__Field_Opordered__comm__semiring_15, cls_NatArith_Oof__nat__eq__iff_0, cls_Ring__and__Field_Oabs__one_0, clsarity_nat_9, cls_Ring__and__Field_Omult__cancel__right2_0, clsrel_Ring__and__Field_Ocomm__ring__1_3, clsrel_Ring__and__Field_Opordered__semiring_11, cls_IntDiv_Ozmod__eq__0D__dest_0, clsarity_set_13, clsrel_Ring__and__Field_Oordered__semidom_32, cls_Parity_Ominus__one__even__power_0, cls_Ring__and__Field_Ofield__mult__cancel__right_0, cls_IntDef_Oof__int__eq__0__iff_0, cls_NatArith_Odiff__Suc__diff__eq1_0, cls_Nat_Oone__le__mult__iff_0, cls_Parity_Oeven__sum_1, cls_Ring__and__Field_Ofield__mult__cancel__right_1, cls_Nat_Odiff__diff__left_0, cls_Parity_Ozero__less__power__eq__number__of_5, clsrel_OrderedGroup_Olordered__ab__group_8, clsrel_Ring__and__Field_Oordered__semidom_5, cls_SetInterval_OatLeast__iff_0, clsarity_IntDef__Oint_33, cls_Parity_Opower__less__zero__eq__number__of_1, cls_SetInterval_OgreaterThanLessThan__iff_1, cls_Parity_Opower__le__zero__eq__number__of_2, cls_Divides_Omod__less_0, cls_Parity_Oeven__zero_0, cls_IntArith_Ozabs__less__one__iff_1, cls_IntDef_Ozero__zle__int_0, cls_NatArith_Oadd__diff__assoc_0, clsrel_Ring__and__Field_Oordered__semidom_6, cls_Parity_Ozero__le__power__eq__number__of_0, clsrel_Ring__and__Field_Ofield_11, clsrel_Ring__and__Field_Oordered__ring__strict_34, cls_Divides_Omod__self_0, clsrel_Ring__and__Field_Oordered__idom_44, cls_IntArith_Onat__1_0, cls_IntDef_Oof__int__le__iff_1, cls_Divides_Odiv__0_0, cls_Divides_Odiv__mult__mult1_0, cls_Nat_OSuc__not__Zero_0, cls_IntDef_Oof__int__0__less__iff_1, cls_Orderings_Oorder__class_Oaxioms__1_0, clsrel_Ring__and__Field_Ofield_22, cls_OrderedGroup_Onprt__0_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, cls_Power_Opower__eq__0__iff_1, cls_IntDiv_Ozdiv__zadd__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_20, clsrel_Power_Orecpower_9, clsrel_Ring__and__Field_Oordered__ring__strict_18, clsrel_OrderedGroup_Olordered__ab__group_2, cls_IntDef_Oof__int__less__0__iff_1, cls_IntDef_Ozle__int_1, cls_Divides_Odiv__mult__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_29, cls_IntDef_Oof__int__le__0__iff_0, cls_SetInterval_OgreaterThanAtMost__iff_1, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2, cls_IntDef_ONats__1_0, cls_OrderedGroup_Oabs__0__eq_1, cls_Nat_Omult__less__cancel1_2, clsrel_OrderedGroup_Olordered__ab__group__abs_17, cls_Nat_Oless__Suc0_1, cls_IntDef_Oint__eq__0__conv_0, cls_Divides_ODIVISION__BY__ZERO__MOD_0, cls_IntDiv_Ozero__le__zpower__abs_0, cls_IntDiv_Ozdiv__self_0, cls_Finite__Set_Ofinite__Diff_0, cls_SetInterval_OatMost__subset__iff_0, cls_SetInterval_OlessThan__0_0, clsrel_Ring__and__Field_Oordered__idom_0, clsrel_OrderedGroup_Olordered__ab__group__abs_7, cls_IntDiv_Ozdiv__zmult__self2_0, clsrel_Ring__and__Field_Oordered__idom_45, cls_Parity_Oeven__nat__Suc_0, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0, cls_Nat_Onat__add__left__cancel_0, cls_Set_ODiff__iff_0, cls_IntDef_Oof__int__0__eq__iff_1, clsarity_IntDef__Oint_30, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, cls_IntDef_Onegative__zle_0, clsarity_nat_13, cls_IntDef_Oof__int__int__eq_0, clsrel_Ring__and__Field_Oordered__semidom_29, cls_Ring__and__Field_Omult__zero__left_0, cls_NatArith_Oof__nat__less__iff_1, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, clsrel_Ring__and__Field_Oordered__idom_34, cls_Divides_Onat__mod__mod__trivial_0, cls_Ring__and__Field_Omult__cancel__right1_0, cls_Nat_Oone__le__mult__iff_2, cls_Parity_Ozero__less__power__eq__number__of_0, cls_Power_Opower__one_0, cls_Parity_Oeven__nat__product_0, cls_IntArith_Ozle__add1__eq__le_0, clsarity_nat_24, cls_List_Olexn_Osimps__1_0, clsrel_OrderedGroup_Ocomm__monoid__mult_1, cls_NatBin_Oone__mod__nat__number__of_1, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsrel_OrderedGroup_Olordered__ab__group__join_9, clsrel_Ring__and__Field_Oordered__idom_6, clsrel_LOrder_Omeet__semilorder_1, clsarity_set_0, clsarity_IntDef__Oint_51, cls_IntArith_Ozle__diff1__eq_1, cls_Nat_OSuc__less__eq_0, cls_Parity_Opower__eq__0__iff__number__of_0, clsarity_nat_4, cls_IntArith_Oone__less__nat__eq_0, clsarity_IntDef__Oint_23, cls_Parity_Oeven__difference_3, clsrel_OrderedGroup_Olordered__ab__group__meet_8, cls_IntDef_Oof__int__diff_0, cls_SetsAndFunctions_Oset__times__mono_0, cls_Nat_Ole0_0, cls_Parity_Oeven__nat__sum_3, clsrel_OrderedGroup_Oab__semigroup__mult_1, clsrel_Ring__and__Field_Ocomm__ring__1_23, clsarity_IntDef__Oint_63, cls_IntDiv_Opower_Osimps__1_0, cls_IntDef_Oint__0__neq__1_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0, cls_NatBin_Oadd__nat__number__of_0, cls_IntDef_Ozless__nat__conj_0, cls_NatBin_Oone__div__nat__number__of_0, cls_Set_Oinsert__iff_0, cls_Set_Oinsert__absorb2_0, cls_Nat_Oop_A_L_Oadd__0_0, clsrel_Ring__and__Field_Oordered__semidom_30, cls_IntDiv_Opos__mod__bound_0, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_Nat_Oadd__gr__0_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3, cls_Set_Onot__psubset__empty_0, cls_IntDef_Ozero__less__nat__eq_0, cls_NatArith_Oof__nat__0__eq__iff_0, cls_List_Ochar_Oinject_1, cls_OrderedGroup_Oabs__of__nonneg_0, cls_Nat_Omult__le__cancel1_2, cls_Power_Opower__increasing__iff_0, cls_Divides_Odiv__le__dividend_0, cls_Parity_Oeven__product_2, clsrel_Power_Orecpower_16, cls_Nat_Oop_A_L_Oadd__Suc_0, clsarity_IntDef__Oint_55, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, cls_SetInterval_OgreaterThanAtMost__empty_0, cls_Nat_Ole__0__eq_1, cls_IntArith_Oint__eq__iff__number__of_2, clsarity_IntDef__Oint_50, cls_NatArith_Oof__nat__diff_0, cls_Set_OPow__empty_0, cls_Parity_Opower__minus__odd_0, clsrel_Ring__and__Field_Ocomm__ring__1_12, clsarity_nat_2, clsrel_Ring__and__Field_Ofield_18, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Set_OpsubsetE_1, cls_Nat_Omult__le__cancel2_0, cls_IntDiv_Ozmod__zminus__zminus_0, cls_Nat_OZero__not__Suc_0, cls_Divides_Omod__mult__self__is__0_0, cls_SetInterval_OatMost__subset__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_2, cls_OrderedGroup_Oabs__idempotent_0, cls_Nat_Omult__less__cancel2_2, cls_Divides_Odiv__self_0, cls_IntDef_Onat__zero_0, cls_Divides_Omod__0_0, cls_OrderedGroup_Oabs__le__zero__iff_1, clsrel_OrderedGroup_Olordered__ab__group__meet_2, cls_Set_Osingleton__insert__inj__eq_2, cls_Parity_Ominus__one__odd__power_0, cls_Nat_OlessI_0, cls_IntDef_Oof__int__eq__0__iff_1, cls_SetInterval_Ofinite__atMost_0, cls_SetInterval_OatLeastAtMost__iff_0, cls_Set_Odouble__complement_0, cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0, cls_Nat_OSuc__pred_0, cls_Nat_Omult__eq__1__iff_1, cls_NatBin_Oeq__number__of__0_1, cls_Nat_Omult__Suc__right_0, cls_Ring__and__Field_Ofield__mult__cancel__left_0, cls_Set_Oinsert__subset_0, cls_Nat_Oone__eq__mult__iff_1, clsrel_Ring__and__Field_Ofield_12, cls_Parity_Opower__even__abs__number__of_0, cls_NatArith_Oof__nat__le__iff_1, cls_Parity_Oeven__neg_1, cls_IntDef_Onegative__zless_0, cls_OrderedGroup_Omeet__0__eq__0_1, cls_OrderedGroup_Oneg__join__eq__meet_0, cls_IntDiv_Ozmod__1_0, cls_IntDef_Onat__zminus__int_0, cls_IntDef_ONats__mult_0, cls_Nat_Omult__is__0_0, cls_IntDiv_Ozmod__zadd__self1_0, cls_IntDef_Oint__le__0__conv_0, clsrel_Ring__and__Field_Ocomm__ring__1_28, cls_SetInterval_OatLeast__0_0, cls_List_Ochar_Osize_0, cls_Parity_Ozero__le__power__eq__number__of_2, cls_IntDef_Oint__le__0__conv_1, cls_Power_Onat__zero__less__power__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_18, cls_IntDef_Ozle__int_0, clsarity_IntDef__Oint_9, clsarity_set_15, cls_List_Odrop__drop_0
% 10.82/3.49 % No. of inferences in proof: 1547
% 10.82/3.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2979 ms resp. 2282 ms w/o parsing
% 11.69/3.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.69/3.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------