TSTP Solution File: ANA045-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA045-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 10:09:00 EDT 2023
% Result : Unsatisfiable 11.45s 3.53s
% Output : Refutation 12.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 588
% Syntax : Number of formulae : 1116 ( 285 unt; 61 typ; 0 def)
% Number of atoms : 2167 ( 578 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 8784 (1046 ~;1112 |; 0 &;6626 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 91 ( 91 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 61 usr; 8 con; 0-3 aty)
% Number of variables : 1680 ( 0 ^;1680 !; 0 ?;1680 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_g_type,type,
v_g: $i > $i ).
thf(v_x_type,type,
v_x: $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_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(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(tc_nat_type,type,
tc_nat: $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(class_LOrder_Ojoin__semilorder_type,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(c_div_type,type,
c_div: $i > $i > $i > $i ).
thf(c_plus_type,type,
c_plus: $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_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $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(c_IntDef_Onat_type,type,
c_IntDef_Onat: $i > $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $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_Opordered__comm__semiring_type,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0__cancel_type,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_LOrder_Olorder_type,type,
class_LOrder_Olorder: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $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_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_IntDef_Oof__int_type,type,
c_IntDef_Oof__int: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__join_type,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
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_HOL_Oinverse_type,type,
c_HOL_Oinverse: $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_emptyset_type,type,
c_emptyset: $i ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Ochar_type,type,
tc_List_Ochar: $i ).
thf(161,axiom,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(892,plain,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(363,axiom,
( ( c_times @ c_1 @ c_1 @ tc_nat )
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
thf(1322,plain,
( ( c_times @ c_1 @ c_1 @ tc_nat )
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(451,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(1501,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(406,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(1411,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
thf(760,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)],[105]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
thf(1454,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)],[429]) ).
thf(265,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
thf(1105,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)],[265]) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
thf(1237,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)],[323]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
thf(893,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)],[162]) ).
thf(184,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
thf(941,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)],[184]) ).
thf(299,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(1179,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(350,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(1295,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(1024,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)],[224]) ).
thf(436,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_1 != c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__neq__zero_0) ).
thf(1469,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_1 != c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oordered__semidom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
thf(628,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)],[46]) ).
thf(228,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
thf(1031,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)],[228]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
thf(777,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)],[112]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
thf(555,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)],[12]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
thf(1211,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)],[313]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
thf(1290,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)],[348]) ).
thf(500,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
thf(1618,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)],[500]) ).
thf(209,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(994,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(400,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).
thf(1401,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)],[400]) ).
thf(480,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
thf(1569,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)],[480]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
thf(878,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)],[155]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(597,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
thf(861,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)],[148]) ).
thf(444,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
thf(1486,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_IntDef_Oint )
| ( ( c_IntDef_Onat @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
thf(582,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)],[23]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
!= ( c_IntDef_Oint @ B ) )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
thf(762,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)],[106]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
thf(1497,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)],[449]) ).
thf(251,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
thf(1078,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(520,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
thf(1671,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)],[520]) ).
thf(496,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(1608,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)],[496]) ).
thf(514,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
thf(1655,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)],[514]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(1137,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
thf(533,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)],[4]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(814,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)],[129]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
thf(538,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)],[6]) ).
thf(179,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_less @ c_0 @ c_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
thf(930,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)],[179]) ).
thf(431,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
thf(1458,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
thf(670,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)],[65]) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
thf(1342,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)],[372]) ).
thf(170,axiom,
! [A: $i] : ( c_IntDef_Oneg @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
thf(913,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)],[170]) ).
thf(307,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
thf(1196,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)],[307]) ).
thf(164,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(898,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
thf(709,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)],[82]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
thf(841,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)],[140]) ).
thf(498,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(1613,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)],[498]) ).
thf(380,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
thf(1359,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)],[380]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(1623,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)],[502]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
thf(973,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)],[199]) ).
thf(158,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(885,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)],[158]) ).
thf(235,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(1046,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(458,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
thf(1518,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_1) ).
thf(1265,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)],[336]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
thf(1287,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)],[347]) ).
thf(416,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_1 @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
thf(1430,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_1 @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(367,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
thf(1330,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)],[367]) ).
thf(360,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_0 != c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).
thf(1313,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_0 != c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
thf(949,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)],[187]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( c_div @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
thf(587,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)],[25]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
thf(619,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)],[41]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
thf(934,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)],[181]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
thf(1191,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)],[305]) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
thf(1462,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)],[433]) ).
thf(277,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
thf(1132,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(470,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
thf(1545,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)],[470]) ).
thf(390,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(1379,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
thf(1087,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)],[256]) ).
thf(328,axiom,
class_Power_Orecpower @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(1247,plain,
class_Power_Orecpower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(362,axiom,
! [A: $i] :
( ~ ( c_less @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
thf(1319,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)],[362]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(1479,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)],[440]) ).
thf(509,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(1641,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)],[509]) ).
thf(448,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).
thf(1494,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)],[448]) ).
thf(321,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(1232,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)],[321]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
thf(817,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)],[130]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
thf(902,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)],[166]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
thf(638,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)],[50]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
thf(853,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)],[145]) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
thf(969,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)],[197]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ B @ c_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
thf(1572,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)],[481]) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
thf(1013,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)],[219]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
thf(770,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)],[109]) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
thf(924,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)],[176]) ).
thf(434,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(1465,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(117,axiom,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_IntDef_Oint @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
thf(789,plain,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_IntDef_Oint @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(27,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
thf(591,plain,
! [A: $i] : ( c_lessequals @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(387,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
thf(1373,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(43,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(623,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
thf(646,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)],[54]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
thf(937,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)],[182]) ).
thf(484,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
thf(1581,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)],[484]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
thf(905,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)],[167]) ).
thf(354,axiom,
class_LOrder_Olorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(1302,plain,
class_LOrder_Olorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(103,axiom,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
thf(756,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)],[103]) ).
thf(517,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(1664,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)],[517]) ).
thf(232,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
thf(1040,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)],[232]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
thf(1109,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)],[267]) ).
thf(505,axiom,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(1632,plain,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(301,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
thf(1183,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(344,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(1283,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(389,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(1377,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)],[389]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
thf(692,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)],[74]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ c_0 @ c_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
thf(734,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)],[92]) ).
thf(425,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).
thf(1447,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)],[425]) ).
thf(150,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(866,plain,
class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( A = c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
thf(1072,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)],[248]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_0) ).
thf(1119,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)],[272]) ).
thf(461,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(1526,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)],[461]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
thf(660,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)],[61]) ).
thf(212,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
thf(998,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)],[212]) ).
thf(206,axiom,
~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
thf(988,plain,
~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(403,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
thf(1405,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)],[403]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
thf(1201,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)],[309]) ).
thf(492,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
thf(1600,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)],[492]) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
thf(1242,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)],[326]) ).
thf(295,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(1169,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
thf(687,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)],[71]) ).
thf(494,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(1604,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)],[494]) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
thf(1206,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)],[311]) ).
thf(174,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/sandbox2/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(920,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)],[174]) ).
thf(2,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(529,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(420,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
thf(1438,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)],[420]) ).
thf(119,axiom,
! [A: $i] :
( ( c_IntDef_Oint @ ( c_Suc @ A ) )
= ( c_plus @ c_1 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
thf(793,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)],[119]) ).
thf(356,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(1306,plain,
class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
thf(1199,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)],[308]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
thf(810,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)],[127]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( A = c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
thf(1338,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)],[370]) ).
thf(359,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(1311,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(245,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).
thf(1067,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
thf(714,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)],[84]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
thf(798,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)],[121]) ).
thf(292,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(1163,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(1274,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)],[340]) ).
thf(394,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(1387,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)],[394]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
thf(825,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)],[133]) ).
thf(222,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(1021,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(233,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(1042,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(378,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(1355,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(332,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
thf(1255,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)],[332]) ).
thf(522,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(1676,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)],[522]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
thf(1217,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)],[315]) ).
thf(131,axiom,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).
thf(820,plain,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(518,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).
thf(1666,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)],[518]) ).
thf(47,axiom,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(630,plain,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
thf(1370,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)],[386]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(729,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)],[90]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ c_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
thf(1560,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)],[476]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
thf(957,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)],[191]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
thf(1223,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)],[318]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_minus @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
thf(746,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)],[98]) ).
thf(257,axiom,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(1091,plain,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(411,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oordered__ring__strict @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
thf(1423,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)],[411]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(916,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)],[172]) ).
thf(493,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(1602,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)],[493]) ).
thf(383,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(1365,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)],[383]) ).
thf(474,axiom,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(1555,plain,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(63,axiom,
! [A: $i] :
( ( c_HOL_Oabs @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
= ( c_IntDef_Oint @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
thf(665,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)],[63]) ).
thf(526,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(1687,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
thf(889,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)],[160]) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
thf(1159,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)],[290]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
thf(551,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)],[10]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
thf(1281,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)],[343]) ).
thf(506,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
thf(1634,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)],[506]) ).
thf(69,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(682,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)],[69]) ).
thf(404,axiom,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(1407,plain,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(401,axiom,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(1402,plain,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(376,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
thf(1350,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(282,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
thf(1143,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)],[282]) ).
thf(56,axiom,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
thf(650,plain,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(465,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(1534,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(39,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
thf(615,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(366,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Onat @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
thf(1328,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)],[366]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
thf(1375,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)],[388]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_0 @ A )
= c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
thf(1111,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)],[268]) ).
thf(412,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
thf(1425,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)],[412]) ).
thf(260,axiom,
c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
thf(1096,plain,
c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
thf(1006,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)],[216]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(96,axiom,
! [A: $i] :
( ~ ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
thf(742,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)],[96]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_less @ c_1 @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
thf(578,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)],[21]) ).
thf(76,axiom,
! [A: $i] :
~ ( c_lessequals @ c_0 @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
thf(697,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)],[76]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( B = c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
thf(1234,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)],[322]) ).
thf(468,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
thf(1541,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)],[468]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
thf(1270,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)],[338]) ).
thf(334,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_div @ A @ A @ tc_nat )
= c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
thf(1259,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)],[334]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
thf(980,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)],[202]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ c_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
thf(1587,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)],[486]) ).
thf(479,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
thf(1567,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)],[479]) ).
thf(381,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_IntDef_Oint )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
thf(1361,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_IntDef_Oint )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ c_1 @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
thf(1292,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)],[349]) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
thf(1075,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)],[249]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(642,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)],[52]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
thf(1414,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)],[408]) ).
thf(485,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
thf(1584,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)],[485]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
thf(1214,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)],[314]) ).
thf(424,axiom,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(1446,plain,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(220,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(1016,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( ( c_times @ B @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
thf(1644,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)],[510]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Suc @ B ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
thf(679,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)],[68]) ).
thf(288,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(1155,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)],[288]) ).
thf(226,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(1028,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(253,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(1082,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
thf(837,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)],[138]) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
thf(701,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)],[78]) ).
thf(285,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(1150,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(351,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(1297,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
thf(654,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)],[58]) ).
thf(87,axiom,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(721,plain,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
thf(1002,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)],[214]) ).
thf(415,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(1429,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(491,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
thf(1599,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)],[491]) ).
thf(113,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(779,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
thf(1393,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)],[397]) ).
thf(364,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(1324,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)],[364]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(1114,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(427,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(1451,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
thf(738,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)],[94]) ).
thf(463,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(1530,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)],[463]) ).
thf(467,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(1539,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)],[467]) ).
thf(430,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(1456,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)],[430]) ).
thf(392,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
thf(1382,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)],[392]) ).
thf(241,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(1060,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_1 @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
thf(1050,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)],[237]) ).
thf(204,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(984,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
thf(911,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)],[169]) ).
thf(368,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(1333,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)],[368]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
thf(1434,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)],[418]) ).
thf(255,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(1086,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(325,axiom,
class_LOrder_Omeet__semilorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(1241,plain,
class_LOrder_Omeet__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
thf(805,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)],[124]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
thf(541,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(477,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(1563,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
thf(765,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)],[107]) ).
thf(499,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(1616,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)],[499]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(773,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)],[110]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
thf(718,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)],[86]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
thf(926,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)],[177]) ).
thf(346,axiom,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(1286,plain,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(230,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).
thf(1035,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(225,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
thf(1026,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)],[225]) ).
thf(294,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
thf(1167,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)],[294]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
thf(953,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)],[189]) ).
thf(302,axiom,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
thf(1185,plain,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(342,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_0) ).
thf(1278,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)],[342]) ).
thf(330,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
thf(1251,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(283,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(1146,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)],[283]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
thf(1103,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)],[264]) ).
thf(316,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
thf(1219,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)],[316]) ).
thf(442,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(1483,plain,
class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( ( c_times @ c_0 @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
thf(1548,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)],[471]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(856,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)],[146]) ).
thf(97,axiom,
c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
thf(745,plain,
c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
thf(573,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)],[19]) ).
thf(72,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(689,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
thf(601,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)],[32]) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
thf(965,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)],[195]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
thf(750,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)],[100]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
thf(1510,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)],[455]) ).
thf(353,axiom,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(1301,plain,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(489,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(1595,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)],[489]) ).
thf(287,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(1154,plain,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(562,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)],[15]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
thf(694,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)],[75]) ).
thf(91,axiom,
( ( c_IntDef_Oint @ c_1 )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
thf(732,plain,
( ( c_IntDef_Oint @ c_1 )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(395,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(1389,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
thf(843,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)],[141]) ).
thf(513,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
thf(1652,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)],[513]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(875,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)],[154]) ).
thf(402,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(1403,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(459,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
thf(1520,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)],[459]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
thf(1124,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)],[274]) ).
thf(319,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
thf(1226,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)],[319]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( ( c_LOrder_Ojoin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
thf(545,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)],[8]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ B @ c_1 @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
thf(1488,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)],[445]) ).
thf(414,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(1428,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
thf(1139,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)],[280]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
thf(1669,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)],[519]) ).
thf(37,axiom,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(611,plain,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(324,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
thf(1239,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)],[324]) ).
thf(258,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
thf(1092,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)],[258]) ).
thf(173,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
thf(919,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_div @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
thf(1058,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)],[240]) ).
thf(266,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
thf(1107,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_div @ A @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
thf(604,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)],[34]) ).
thf(306,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(1194,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
thf(1209,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)],[312]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
thf(831,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)],[135]) ).
thf(405,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Opprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
thf(1408,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)],[405]) ).
thf(218,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(1011,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(375,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(1349,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(447,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(1492,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
thf(1122,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)],[273]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
thf(599,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)],[31]) ).
thf(357,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(1307,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
thf(784,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)],[115]) ).
thf(271,axiom,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
thf(1117,plain,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(236,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).
thf(1048,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
thf(736,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)],[93]) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
thf(990,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)],[207]) ).
thf(211,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(996,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(156,axiom,
( ( c_IntDef_Onat @ c_1 )
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
thf(880,plain,
( ( c_IntDef_Onat @ c_1 )
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(55,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(649,plain,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(149,axiom,
! [A: $i] :
( ( A = c_0 )
| ( ( c_div @ A @ A @ tc_IntDef_Oint )
= c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
thf(863,plain,
! [A: $i] :
( ( A = c_0 )
| ( ( c_div @ A @ A @ tc_IntDef_Oint )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(1175,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
thf(1080,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)],[252]) ).
thf(104,axiom,
! [A: $i] :
~ ( c_less @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
thf(758,plain,
! [A: $i] :
~ ( c_less @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
thf(609,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)],[36]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
thf(726,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)],[89]) ).
thf(42,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(621,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
thf(848,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)],[143]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(626,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)],[45]) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
thf(1344,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)],[373]) ).
thf(432,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(1460,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(185,axiom,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(943,plain,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Oop_Amod @ ( c_times @ A @ B @ tc_nat ) @ B @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
thf(1177,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)],[298]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
thf(932,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)],[180]) ).
thf(527,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(1688,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
thf(858,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)],[147]) ).
thf(475,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
thf(1557,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)],[475]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
thf(1029,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)],[227]) ).
thf(163,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(895,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
thf(1171,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)],[296]) ).
thf(203,axiom,
c_lessequals @ ( c_IntDef_Oint @ c_0 ) @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
thf(983,plain,
c_lessequals @ ( c_IntDef_Oint @ c_0 ) @ c_0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
thf(1396,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)],[398]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
thf(959,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)],[192]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
thf(768,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)],[108]) ).
thf(205,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(986,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(213,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).
thf(1000,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)],[213]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
thf(922,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)],[175]) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
thf(1044,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)],[234]) ).
thf(327,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(1245,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)],[327]) ).
thf(244,axiom,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(1066,plain,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(462,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
thf(1528,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)],[462]) ).
thf(407,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(1413,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(1626,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)],[503]) ).
thf(293,axiom,
class_Power_Orecpower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(1166,plain,
class_Power_Orecpower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(26,axiom,
! [A: $i] :
( ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
thf(589,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)],[26]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
thf(531,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)],[3]) ).
thf(435,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
thf(1467,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)],[435]) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
thf(795,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)],[120]) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
thf(1420,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)],[410]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ B @ c_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
thf(1684,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)],[525]) ).
thf(278,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
thf(1134,plain,
c_0 != c_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(812,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)],[128]) ).
thf(40,axiom,
( ( c_IntDef_Onat @ c_0 )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
thf(617,plain,
( ( c_IntDef_Onat @ c_0 )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(183,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/sandbox2/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(939,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)],[183]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
thf(1472,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)],[437]) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
thf(1018,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)],[221]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
thf(754,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)],[102]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
thf(553,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)],[11]) ).
thf(472,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
thf(1551,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)],[472]) ).
thf(62,axiom,
! [A: $i] :
( ( c_div @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
thf(663,plain,
! [A: $i] :
( ( c_div @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
thf(548,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)],[9]) ).
thf(300,axiom,
( ( c_Suc @ c_0 )
= ( c_times @ c_1 @ c_1 @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
thf(1181,plain,
( ( c_Suc @ c_0 )
= ( c_times @ c_1 @ c_1 @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
thf(823,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)],[132]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
thf(580,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)],[22]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
thf(640,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)],[51]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
thf(707,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)],[81]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
thf(887,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)],[159]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
thf(971,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)],[198]) ).
thf(511,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(1647,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)],[511]) ).
thf(385,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(1368,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(443,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
thf(1484,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)],[443]) ).
thf(262,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
thf(1098,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)],[262]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
thf(712,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)],[83]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
thf(557,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)],[13]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
thf(690,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)],[73]) ).
thf(457,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(1516,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)],[457]) ).
thf(247,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1070,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
thf(872,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)],[153]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
thf(705,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)],[80]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= ( c_times @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(1611,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)],[497]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(673,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)],[66]) ).
thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
thf(1432,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)],[417]) ).
thf(507,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(1637,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)],[507]) ).
thf(118,axiom,
! [A: $i] :
( ( c_IntDef_Onat @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) )
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
thf(791,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)],[118]) ).
thf(303,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(1188,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
thf(585,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)],[24]) ).
thf(335,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
thf(1262,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)],[335]) ).
thf(369,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).
thf(1336,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)],[369]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
thf(1053,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)],[238]) ).
thf(450,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(1499,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(576,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)],[20]) ).
thf(515,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(1658,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)],[515]) ).
thf(188,axiom,
( c_1
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(951,plain,
( c_1
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(808,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)],[126]) ).
thf(469,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(1543,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)],[469]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
thf(1257,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)],[333]) ).
thf(79,axiom,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
thf(703,plain,
! [A: $i] :
( ( c_div @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
thf(613,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)],[38]) ).
thf(413,axiom,
class_LOrder_Ojoin__semilorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(1427,plain,
class_LOrder_Ojoin__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(452,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(1504,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
thf(1008,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)],[217]) ).
thf(18,axiom,
! [A: $i] :
( ( c_div @ A @ c_1 @ tc_IntDef_Oint )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
thf(571,plain,
! [A: $i] :
( ( c_div @ A @ c_1 @ tc_IntDef_Oint )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(595,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)],[29]) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
thf(1272,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)],[339]) ).
thf(281,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
thf(1141,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)],[281]) ).
thf(466,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
thf(1536,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)],[466]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
thf(656,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)],[59]) ).
thf(223,axiom,
c_less @ c_0 @ c_1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
thf(1023,plain,
c_less @ c_0 @ c_1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(317,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
thf(1221,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ A @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(345,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
thf(1284,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)],[345]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(1094,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)],[259]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
thf(978,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)],[201]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
thf(845,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)],[142]) ).
thf(473,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(1553,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)],[473]) ).
thf(289,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(1157,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(200,axiom,
! [A: $i] :
~ ( c_IntDef_Oneg @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
thf(976,plain,
! [A: $i] :
~ ( c_IntDef_Oneg @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
thf(1126,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)],[275]) ).
thf(304,axiom,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
thf(1189,plain,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(428,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(1453,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_1 @ B @ A )
= c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
thf(1316,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)],[361]) ).
thf(512,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
thf(1649,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)],[512]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
thf(1084,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)],[254]) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
thf(1390,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)],[396]) ).
thf(482,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
thf(1575,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)],[482]) ).
thf(365,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(1326,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)],[365]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(961,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)],[193]) ).
thf(194,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ c_1 @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
thf(963,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)],[194]) ).
thf(439,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
thf(1476,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)],[439]) ).
thf(508,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(1639,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(441,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(1481,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
thf(652,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)],[57]) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(1629,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)],[504]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
thf(632,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)],[48]) ).
thf(460,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
thf(1523,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)],[460]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( c_lessequals @ ( c_IntDef_Oint @ A ) @ c_0 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
thf(786,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)],[116]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
thf(781,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)],[114]) ).
thf(210,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(995,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(341,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(1276,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
thf(1590,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)],[487]) ).
thf(331,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(1253,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
thf(699,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)],[77]) ).
thf(371,axiom,
class_LOrder_Olorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(1341,plain,
class_LOrder_Olorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(99,axiom,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(748,plain,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(242,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
thf(1062,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)],[242]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= ( c_times @ B @ c_0 @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(1508,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)],[454]) ).
thf(186,axiom,
! [A: $i] :
( ( c_lessequals @ c_0 @ A @ tc_IntDef_Oint )
| ( ( c_IntDef_Oint @ ( c_IntDef_Onat @ A ) )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
thf(946,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)],[186]) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
thf(1101,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)],[263]) ).
thf(446,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(1491,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
thf(568,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)],[17]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
thf(914,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)],[171]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint )
!= ( c_IntDef_Oint @ B ) )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
thf(667,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)],[64]) ).
thf(421,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
thf(1440,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)],[421]) ).
thf(250,axiom,
class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(1077,plain,
class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(456,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/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).
thf(1513,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)],[456]) ).
thf(70,axiom,
! [A: $i] :
( ( ( c_IntDef_Oint @ A )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
thf(684,plain,
! [A: $i] :
( ( ( c_IntDef_Oint @ A )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(358,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
thf(1309,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)],[358]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
thf(536,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)],[5]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
thf(899,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)],[165]) ).
thf(516,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
thf(1661,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)],[516]) ).
thf(423,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(1444,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)],[423]) ).
thf(422,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(1442,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)],[422]) ).
thf(85,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(716,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)],[85]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
thf(1161,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)],[291]) ).
thf(270,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(1116,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
thf(752,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)],[101]) ).
thf(483,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(1578,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)],[483]) ).
thf(523,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs @ c_1 @ A )
= c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
thf(1678,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)],[523]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
thf(1229,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)],[320]) ).
thf(355,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
thf(1303,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)],[355]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( B = c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
thf(1248,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)],[329]) ).
thf(151,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(867,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(603,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)],[33]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(833,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)],[136]) ).
thf(196,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(967,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(261,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(1097,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(137,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(835,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(488,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(1593,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)],[488]) ).
thf(391,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(1380,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
thf(1148,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)],[284]) ).
thf(521,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(1673,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)],[521]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(419,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
thf(1436,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
thf(801,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)],[122]) ).
thf(382,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
thf(1363,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)],[382]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(807,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)],[125]) ).
thf(239,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
thf(1056,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)],[239]) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
thf(1033,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)],[229]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
thf(828,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)],[134]) ).
thf(243,axiom,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(1065,plain,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(190,axiom,
! [A: $i] :
( ( c_div @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
thf(955,plain,
! [A: $i] :
( ( c_div @ A @ ( c_Suc @ c_0 ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
thf(1346,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)],[374]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
thf(928,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)],[178]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(635,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_2) ).
thf(1473,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)],[438]) ).
thf(95,axiom,
( ( c_IntDef_Oint @ c_0 )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
thf(740,plain,
( ( c_IntDef_Oint @ c_0 )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
thf(1352,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)],[377]) ).
thf(276,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Onprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
thf(1129,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)],[276]) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
thf(1268,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)],[337]) ).
thf(286,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(1152,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(464,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(1532,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(393,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
thf(1384,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)],[393]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( c_lessequals @ c_0 @ ( c_times @ A @ ( c_HOL_Oabs @ ( v_g @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(528,plain,
! [A: $i] :
~ ( c_lessequals @ c_0 @ ( c_times @ A @ ( c_HOL_Oabs @ ( v_g @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
thf(644,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)],[53]) ).
thf(379,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(1357,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
thf(723,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)],[88]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
thf(850,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)],[144]) ).
thf(352,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
thf(1299,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)],[352]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(607,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(44,axiom,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(624,plain,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(839,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)],[139]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( ( c_LOrder_Omeet @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
thf(908,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)],[168]) ).
thf(208,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(992,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(490,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(1597,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
thf(1004,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)],[215]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
thf(1505,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)],[453]) ).
thf(399,axiom,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
thf(1399,plain,
! [A: $i] :
( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(501,axiom,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(1621,plain,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(495,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(1606,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)],[495]) ).
thf(123,axiom,
( ( c_uminus @ ( c_IntDef_Oint @ c_0 ) @ tc_IntDef_Oint )
= ( c_IntDef_Oint @ c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
thf(803,plain,
( ( c_uminus @ ( c_IntDef_Oint @ c_0 ) @ tc_IntDef_Oint )
= ( c_IntDef_Oint @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(384,axiom,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(1367,plain,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(524,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
= ( c_HOL_Oabs @ c_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
thf(1681,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)],[524]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
thf(676,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)],[67]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
thf(592,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)],[28]) ).
thf(246,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(1069,plain,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_2) ).
thf(882,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)],[157]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
thf(1417,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)],[409]) ).
thf(60,axiom,
c_Parity_Oeven @ c_0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
thf(659,plain,
c_Parity_Oeven @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(478,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
thf(1565,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)],[478]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
thf(1037,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)],[231]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
thf(775,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)],[111]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(560,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)],[14]) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
thf(1204,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)],[310]) ).
thf(426,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(1449,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)],[426]) ).
thf(1690,plain,
$false,
inference(e,[status(thm)],[892,1322,1501,1411,760,1454,1105,1237,893,941,1179,1295,1024,1469,628,1031,777,555,1211,1290,1618,994,1401,1569,878,597,861,1486,582,762,1497,1078,1671,1608,1655,1137,533,814,538,930,1458,670,1342,913,1196,898,709,841,1613,1359,1623,973,885,1046,1518,1265,1287,1430,1330,1313,949,587,619,934,1191,1462,1132,1545,1379,1087,1247,1319,1479,1641,1494,1232,817,902,638,853,969,1572,1013,770,924,1465,789,591,1373,623,646,937,1581,905,1302,756,1664,1040,1109,1632,1183,1283,1377,692,734,1447,866,1072,1119,1526,660,998,988,1405,1201,1600,1242,1169,687,1604,1206,920,529,1438,793,1306,1199,810,1338,1311,1067,714,798,1163,1274,1387,825,1021,1042,1355,1255,1676,1217,820,1666,630,1370,729,1560,957,1223,746,1091,1423,916,1602,1365,1555,665,1687,889,1159,551,1281,1634,682,1407,1402,1350,1143,650,1534,615,1328,1375,1111,1425,1096,1006,869,742,578,697,1234,1541,1270,1259,980,1587,1567,1361,1292,1075,642,1414,1584,1214,1446,1016,1644,679,1155,1028,1082,837,701,1150,1297,654,721,1002,1429,1599,779,1393,1324,1114,1451,738,1530,1539,1456,1382,1060,1050,984,911,1333,1434,1086,1241,805,541,1563,765,1616,773,718,926,1286,1035,1026,1167,953,1185,1278,1251,1146,1103,1219,1483,1548,856,745,573,689,601,965,750,1510,1301,1595,1154,562,694,732,1389,843,1652,875,1403,1520,1124,1226,545,1488,1428,1139,1669,611,1239,1092,919,1058,1107,604,1194,1209,831,1408,1011,1349,1492,1122,599,1307,784,1117,1048,736,990,996,880,649,863,1175,1080,758,609,726,621,848,626,1344,1460,943,1177,932,1688,858,1557,1029,895,1171,983,1396,959,768,986,1000,922,1044,1245,1066,1528,1413,1626,1166,589,531,1467,795,1420,1684,1134,812,617,939,1472,1018,754,553,1551,663,548,1181,823,580,640,707,887,971,1647,1368,1484,1098,712,557,690,1516,1070,872,705,1611,673,1432,1637,791,1188,585,1262,1336,1053,1499,576,1658,951,808,1543,1257,703,613,1427,1504,1008,571,595,1272,1141,1536,656,1023,1221,1284,1094,978,845,1553,1157,976,1126,1189,1453,1316,1649,1084,1390,1575,1326,961,963,1476,1639,1481,652,1629,632,1523,786,781,995,1276,1590,1253,699,1341,748,1062,1508,946,1101,1491,568,914,667,1440,1077,1513,684,1309,536,899,1661,1444,1442,716,1161,1116,752,1578,1678,1229,1303,1248,867,603,833,967,1097,835,1593,1380,1148,1673,564,1436,801,1363,807,1056,1033,828,1065,955,1346,928,635,1473,740,1352,1129,1268,1152,1532,1384,528,644,1357,723,850,1299,607,624,839,908,992,1597,1004,1505,1399,1621,1606,803,1367,1681,676,592,1069,882,1417,659,1565,1037,775,560,1204,1449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA045-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 17:52:13 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.83/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.23/1.18 % [INFO] Parsing done (324ms).
% 2.23/1.19 % [INFO] Running in sequential loop mode.
% 2.72/1.41 % [INFO] eprover registered as external prover.
% 2.72/1.41 % [INFO] cvc4 registered as external prover.
% 2.72/1.41 % [INFO] Scanning for conjecture ...
% 3.28/1.57 % [INFO] Found a conjecture and 2782 axioms. Running axiom selection ...
% 4.25/1.77 % [INFO] Axiom selection finished. Selected 525 axioms (removed 2257 axioms).
% 4.52/1.91 % [INFO] Problem is propositional (TPTP CNF).
% 4.71/1.92 % [INFO] Type checking passed.
% 4.71/1.93 % [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 ...
% 11.45/3.52 % External prover 'e' found a proof!
% 11.45/3.52 % [INFO] Killing All external provers ...
% 11.45/3.52 % Time passed: 2992ms (effective reasoning time: 2325ms)
% 11.45/3.52 % 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)>
% 11.45/3.53 % Axioms used in derivation (525): clsarity_IntDef__Oint_34, cls_IntDef_Ozero__less__int__conv_0, cls_Parity_Opower__less__zero__eq__number__of_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_Parity_Opower__le__zero__eq__number__of_1, cls_Power_Opower__0__Suc_0, cls_Nat_Oone__eq__mult__iff_0, cls_NatArith_Oadd__diff__assoc2_0, cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0, cls_Power_Onat__zero__less__power__iff_2, cls_Nat_Onot__less0_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_IntDef_Ozless__nat__conj_1, cls_Parity_Oeven__nat__power_2, cls_IntDef_Ozless__int_0, cls_IntDef_Oint__eq__0__conv_1, cls_Parity_Oeven__sum_2, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Nat_Onat__add__left__cancel__less_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, clsrel_Ring__and__Field_Oordered__idom_12, clsrel_Ring__and__Field_Ofield_8, 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_IntDiv_Ozdiv__1_0, cls_IntDef_Oint__nat__eq_0, cls_Nat_Omult__le__cancel1_1, cls_Parity_Oeven__nat__product_1, cls_Nat_Oless__one_1, clsrel_Power_Orecpower_21, clsrel_Ring__and__Field_Oordered__semidom_28, cls_Nat_Odiff__is__0__eq_0, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_OrderedGroup_Opprt__eq__id_0, cls_Parity_Oeven__nat__sum_1, cls_Nat_OSuc__Suc__eq_0, clsarity_nat_40, 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_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_Ring__and__Field_Oordered__ring__strict_22, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_IntDef_Onegative__eq__positive_0, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, cls_IntDiv_ODIVISION__BY__ZERO_0, 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_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__0__eq_0, clsarity_IntDef__Oint_56, cls_IntDef_Oint__less__0__conv_0, cls_OrderedGroup_Onprt__mono_0, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_NatBin_Oeq__0__number__of_1, cls_OrderedGroup_Oneg__meet__eq__join_0, cls_Ring__and__Field_Omult__cancel__left1_2, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Onat__le__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_Nat_Ozero__less__diff_1, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_IntDiv_Ozmod__zmult__self2_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, cls_Power_Opower__one__right_0, cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0, cls_IntDef_Oof__int__less__iff_0, clsarity_nat_29, cls_Nat_Omult__less__cancel2_1, cls_NatArith_Odiff__diff__right_0, cls_Divides_Odiv__mult__self__is__m_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_Parity_Oeven__power_2, cls_Nat_Omult__0__right_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_OrderedGroup_Omeet__0__eq__0_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_NatBin_Odiv__nat__number__of_1, clsrel_Ring__and__Field_Ofield_17, cls_Power_Opower__strict__increasing__iff_0, cls_Power_Ozero__le__power__abs_0, 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_Power_Opower__increasing__iff_1, cls_Nat_Odiff__Suc__Suc_0, clsrel_Ring__and__Field_Oordered__semidom_35, cls_Nat_Omult__eq__1__iff_2, cls_Nat_Omult__le__cancel1_0, cls_IntDef_Oof__int__le__0__iff_1, cls_Parity_Oeven__neg_0, cls_Nat_Oless__one_0, cls_IntDiv_Omod__mod__trivial_0, cls_IntDef_Oint__nat__eq_1, clsarity_IntDef__Oint_48, clsrel_OrderedGroup_Olordered__ab__group_6, cls_Nat_Ole__add__diff__inverse2_0, cls_Parity_Ozero__less__power__nat__eq__number__of_1, clsarity_IntDef__Oint_58, 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, cls_Parity_Ozero__less__power__nat__eq__number__of_0, clsrel_Ring__and__Field_Oordered__idom_51, cls_Power_Onat__one__le__power_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, 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_Oordered__idom_42, clsrel_Ring__and__Field_Oordered__idom_52, cls_Parity_Oeven__sum_0, cls_Parity_Oeven__product_0, cls_IntDef_Oof__int__less__iff_1, clsrel_Ring__and__Field_Oordered__idom_36, cls_Divides_Omod__mult__self1_0, cls_Power_Ozero__less__power__abs__iff_0, cls_OrderedGroup_Ozero__le__pprt_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, cls_Nat_Oadd__is__0_1, cls_Parity_Opower__eq__0__iff__number__of_1, cls_Parity_Oeven__nat__power_1, 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_Nat_Omult__le__cancel2_2, clsrel_Ring__and__Field_Oordered__idom_47, cls_IntDef_Oof__int__0__le__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_36, 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_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, clsrel_Ring__and__Field_Oordered__idom_18, clsrel_Ring__and__Field_Oordered__ring__strict_16, cls_Ring__and__Field_Omult__cancel__right1_1, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_Divides_Odiv__mult__self1__is__m_0, cls_NatBin_Omod__nat__number__of_1, 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_NatArith_Odiff__less_0, cls_Divides_ODIVISION__BY__ZERO__DIV_0, cls_Nat_Ozero__less__diff_0, cls_Parity_Oeven__sum_3, cls_Divides_Omod__add__self2_0, 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_Ring__and__Field_Omult__cancel__left1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_6, cls_IntDef_Oabs__int__eq_0, cls_Parity_Opower__le__zero__eq__number__of_4, 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, clsarity_nat_37, cls_Parity_Oeven__nat__zero_0, cls_IntDef_Oint__int__eq_0, clsrel_LOrder_Olorder_0, cls_Nat_Omult__less__cancel1_0, cls_Ring__and__Field_Ozero__le__one_0, cls_Divides_Omod__mult__self1__is__0_0, cls_Parity_Opower__0__left__number__of_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, cls_Divides_Omod__less__divisor_0, cls_Nat_Omult__cancel2_0, clsarity_IntDef__Oint_37, clsrel_Ring__and__Field_Oordered__semidom_12, cls_Ring__and__Field_Omult__cancel__left2_0, cls_Parity_Oeven__power_1, clsarity_nat_6, cls_Power_Opower__strict__increasing__iff_1, cls_IntDef_Ozless__nat__conj_2, clsarity_nat_43, cls_NatBin_Oint__nat__number__of_0, cls_IntDef_Onegative__eq__positive_1, cls_NatBin_Oeq__nat__number__of_10, cls_Divides_Omod__1_0, cls_Nat_Omult__cancel2_1, cls_IntArith_Oone__less__nat__eq_1, clsrel_OrderedGroup_Olordered__ab__group__abs_16, cls_IntArith_Oint__eq__iff__number__of_0, cls_Nat_Onat__0__less__mult__iff_1, clsrel_Power_Orecpower_3, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_Ring__and__Field_Oordered__idom_46, clsarity_nat_45, clsrel_OrderedGroup_Olordered__ab__group__meet_15, cls_IntDiv_Ozmod__zero_0, cls_Nat_OSuc__diff__diff_0, cls_OrderedGroup_Opprt__0_0, cls_NatBin_Omod__nat__number__of_2, clsarity_IntDef__Oint_18, clsarity_nat_34, cls_Parity_Ozero__less__power__nat__eq__number__of_2, cls_Nat_OSuc__le__mono_1, clsrel_Ring__and__Field_Oordered__ring__strict_35, clsarity_nat_17, 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_IntDef_Oof__int__less__0__iff_0, cls_OrderedGroup_Opprt__eq__0_0, cls_IntDiv_Ozdiv__zmult__self1_0, cls_NatBin_Onat__number__of_0, clsrel_Ring__and__Field_Oordered__semidom_36, cls_Divides_Omod__mult__self2_0, cls_OrderedGroup_Oabs__of__nonpos_0, cls_NatArith_Odiff__Suc__diff__eq2_0, cls_IntArith_Ozle__add1__eq__le_1, 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, clsarity_IntDef__Oint_54, cls_IntArith_Ozabs__less__one__iff_0, 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, clsrel_OrderedGroup_Olordered__ab__group__join_16, cls_NatBin_Oone__mod__nat__number__of_0, cls_OrderedGroup_Oabs__minus__cancel_0, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_Parity_Opower__le__zero__eq__number__of_3, cls_Nat_Oless__Suc0_0, cls_IntDef_Oint__1_0, cls_IntDef_Onot__zle__0__negative_0, cls_OrderedGroup_Ozero__less__abs__iff_1, 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, clsrel_Ring__and__Field_Oordered__ring__strict_24, cls_NatArith_Odiff__diff__cancel_0, cls_OrderedGroup_Oabs__eq__0_1, cls_Ring__and__Field_Omult__cancel__left1_0, cls_Ring__and__Field_Onot__one__less__zero_0, cls_NatBin_Omod__nat__number__of_0, cls_Parity_Oeven__nat__sum_2, clsrel_OrderedGroup_Olordered__ab__group_15, clsrel_Ring__and__Field_Oordered__idom_41, cls_IntDef_Onot__int__zless__negative_0, clsarity_IntDef__Oint_32, clsrel_Ring__and__Field_Oordered__ring__strict_28, 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, 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, clsarity_IntDef__Oint_22, cls_Nat_Omult__le__cancel2_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, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_IntDiv_Oneg__mod__sign_0, clsrel_Ring__and__Field_Oordered__idom_8, cls_Nat_Onot__gr0_1, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, cls_Nat_Onot__add__less2_0, cls_Nat_Oadd__Suc__right_0, cls_IntDiv_Ozero__less__zpower__abs__iff_0, clsrel_Ring__and__Field_Oordered__semidom_26, cls_IntDef_Ozless__int_1, cls_IntDiv_Ozmod__eq__0D__dest_0, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, cls_Ring__and__Field_Oabs__one_0, clsarity_nat_9, cls_Ring__and__Field_Omult__cancel__right2_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_Ring__and__Field_Oordered__semidom_5, clsarity_IntDef__Oint_33, cls_Parity_Opower__less__zero__eq__number__of_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, 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_OrderedGroup_Oabs__0__eq_1, cls_Nat_Omult__less__cancel1_2, cls_IntDef_Oof__int__0__less__iff_1, 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_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, clsrel_Ring__and__Field_Oordered__semidom_29, cls_Ring__and__Field_Omult__zero__left_0, clsrel_OrderedGroup_Olordered__ab__group__abs_7, cls_IntDiv_Ozdiv__zmult__self2_0, cls_Parity_Oeven__nat__Suc_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, 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_IntDef_Oof__int__0__eq__iff_1, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, cls_IntDef_Onegative__zle_0, clsarity_nat_13, 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, clsarity_IntDef__Oint_51, cls_IntArith_Ozle__diff1__eq_1, cls_Nat_Ole0_0, cls_Nat_OSuc__less__eq_0, cls_Parity_Oeven__nat__sum_3, cls_Parity_Opower__eq__0__iff__number__of_0, clsarity_nat_4, cls_IntArith_Oone__less__nat__eq_0, cls_NatBin_Oone__div__nat__number__of_0, cls_Nat_Oop_A_L_Oadd__0_0, clsarity_IntDef__Oint_23, cls_Parity_Oeven__difference_3, cls_Nat_Oadd__gr__0_1, 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, clsrel_Ring__and__Field_Oordered__semidom_30, cls_IntDiv_Opos__mod__bound_0, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_IntDef_Ozero__less__nat__eq_0, clsarity_IntDef__Oint_50, 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_Nat_Ole__0__eq_1, cls_IntArith_Oint__eq__iff__number__of_2, clsrel_Ring__and__Field_Ofield_18, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Nat_Omult__le__cancel2_0, clsrel_OrderedGroup_Olordered__ab__group__meet_2, cls_IntDiv_Ozmod__zminus__zminus_0, cls_Nat_OZero__not__Suc_0, cls_Divides_Omod__mult__self__is__0_0, clsrel_Ring__and__Field_Oordered__ring__strict_2, cls_Nat_OlessI_0, cls_IntDef_Oof__int__eq__0__iff_1, 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, 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_IntDef_Oint__le__0__conv_0, cls_Nat_Oone__eq__mult__iff_1, cls_List_Ochar_Osize_0, clsrel_Ring__and__Field_Ofield_12, cls_Parity_Opower__even__abs__number__of_0, 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_List_Odrop__drop_0, cls_Nat_Omult__is__0_0, cls_IntDiv_Ozmod__zadd__self1_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
% 11.45/3.53 % No. of inferences in proof: 1055
% 11.45/3.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2992 ms resp. 2325 ms w/o parsing
% 12.42/3.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.42/3.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------