TSTP Solution File: LCL754-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL754-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:31:26 EDT 2023
% Result : Unsatisfiable 12.53s 3.82s
% Output : Refutation 13.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 475
% Syntax : Number of formulae : 903 ( 217 unt; 48 typ; 0 def)
% Number of atoms : 1887 ( 546 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 10180 (1008 ~;1032 |; 0 &;8140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 5 con; 0-3 aty)
% Number of variables : 2110 ( 0 ^;2110 !; 0 ?;2110 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
thf(v_ra_type,type,
v_ra: $i ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(v_ia_type,type,
v_ia: $i ).
thf(v_ja_type,type,
v_ja: $i ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i > $i > $i ).
thf(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_Lambda_Oliftn_type,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(c_Lambda_Osubstn_type,type,
c_Lambda_Osubstn: $i > $i > $i > $i ).
thf(c_List_Olast_type,type,
c_List_Olast: $i > $i > $i ).
thf(c_List_Oupt_type,type,
c_List_Oupt: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Lambda_Osko__Lambda__Xbeta__cases__2__1_type,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).
thf(388,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(161,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(809,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(394,axiom,
! [A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) )
| ~ ( c_InductTermi_OIT @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(1337,plain,
! [A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) )
| ~ ( c_InductTermi_OIT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(1411,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(257,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1024,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(846,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(80,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(628,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(518,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(87,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(645,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(892,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(296,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(1105,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(375,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(1295,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(977,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(582,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(248,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1005,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(683,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(278,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1068,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(280,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(1073,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(188,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(873,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(1173,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(7,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(440,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(380,axiom,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(1305,plain,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(597,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(283,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(1078,plain,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(320,axiom,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(1164,plain,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(715,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(698,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(945,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(930,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(199,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(898,plain,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(782,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(176,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(841,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(973,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(372,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(1287,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(570,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(75,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(619,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(333,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oupt @ A @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__upt_0) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oupt @ A @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1059,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(421,axiom,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(1409,plain,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(1264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(208,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(917,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(751,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(817,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(559,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1147,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(881,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(252,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(1013,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(770,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(924,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(1373,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(77,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(623,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(646,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OApp @ B @ C ) @ D )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ A @ B @ D ) @ ( c_Lambda_Oliftn @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(937,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OApp @ B @ C ) @ D )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ A @ B @ D ) @ ( c_Lambda_Oliftn @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ B ) @ ( c_Suc @ C ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ C ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ B ) @ ( c_Suc @ C ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ C ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(687,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(227,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(956,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(866,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(527,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1119,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(774,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1,negated_conjecture,
c_InductTermi_OIT @ v_ra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(428,plain,
c_InductTermi_OIT @ v_ra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(210,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(920,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(678,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(94,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(661,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
!= ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
!= ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(118,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(714,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(452,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
= B )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
= B )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(268,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(1047,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(319,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(1163,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_0) ).
thf(1387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(1091,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(1355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(1217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_ra @ ( c_Lambda_OdB_OVar @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(429,plain,
! [B: $i,A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_ra @ ( c_Lambda_OdB_OVar @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ A @ B ) @ C )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) @ ( c_Lambda_Olift @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ A @ B ) @ C )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) @ ( c_Lambda_Olift @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(260,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(1032,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(852,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(376,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1296,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(889,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(461,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(1027,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) )
| ~ ( c_InductTermi_OIT @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) )
| ~ ( c_InductTermi_OIT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(289,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(1089,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(254,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(1017,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(1328,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(237,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(980,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ A @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ A @ B ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ A @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ A @ B ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(857,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(578,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(1259,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(884,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(1182,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(642,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(1414,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(342,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1214,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(1292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(933,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(554,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(136,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_Suc__le__mono_0) ).
thf(753,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)],[136]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(901,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(105,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(686,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(281,axiom,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1075,plain,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(264,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(1039,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(970,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(174,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(837,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(1114,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(361,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1263,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(1382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(1266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1131,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(270,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(1050,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(1246,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(205,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(911,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(605,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(1318,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(351,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1241,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(633,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(331,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(1187,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(321,axiom,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1167,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(794,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(213,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(926,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(3,negated_conjecture,
~ ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ v_ra ) @ ( c_Lambda_OdB_OVar @ v_ia ) @ v_ja ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(430,plain,
~ ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ v_ra ) @ ( c_Lambda_OdB_OVar @ v_ia ) @ v_ja ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(689,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(444,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(965,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(134,axiom,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(750,plain,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(772,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(169,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(826,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(346,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1226,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(228,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(958,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(383,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1312,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(1107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(1332,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(804,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(141,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(764,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(334,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(1194,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(1282,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(784,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(1011,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(1048,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(996,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(312,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ C ) @ ( c_Suc @ D ) ) @ ( c_Lambda_Osubst @ E @ B @ D ) @ C )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ E @ C ) @ B @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(1144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ C ) @ ( c_Suc @ D ) ) @ ( c_Lambda_Osubst @ E @ B @ D ) @ C )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ E @ C ) @ B @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ C )
= ( c_Lambda_Osubst @ A @ ( c_Lambda_Oliftn @ C @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(1376,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ C )
= ( c_Lambda_Osubst @ A @ ( c_Lambda_Oliftn @ C @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(863,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(71,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(609,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ D ) @ ( c_Lambda_Olift @ B @ D ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(1325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ D ) @ ( c_Lambda_Olift @ B @ D ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(198,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(895,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) @ ( c_Lambda_Osubst @ D @ B @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(1344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) @ ( c_Lambda_Osubst @ D @ B @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(1112,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(626,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(216,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(932,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(1066,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(253,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(1015,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(240,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(986,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(93,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(658,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(336,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(1198,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(193,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(883,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(473,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(722,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(261,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1034,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(285,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1081,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(617,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(48,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(553,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(59,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(580,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1070,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(705,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(993,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(117,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(712,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(557,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ B @ A ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ B @ A ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(114,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(707,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ A @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ A @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(673,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(330,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(1186,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(502,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(1235,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(1220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OAbs @ B ) @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(1358,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OAbs @ B ) @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(358,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(1257,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(991,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(408,axiom,
! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(1372,plain,
! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(366,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1272,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(1180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(903,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1189,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(1316,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ A ) @ B @ C )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ A ) @ B @ C )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(1289,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(177,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(844,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(62,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_Suc__le__mono_1) ).
thf(588,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)],[62]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(961,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(731,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(786,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(381,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(1308,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(282,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1077,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(832,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(1309,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(1116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(347,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(128,axiom,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(735,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(245,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(999,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(950,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(292,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(1097,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(854,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(379,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(1303,plain,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(767,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(664,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(828,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ D @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ D @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(209,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(918,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(157,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(801,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(437,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(1129,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(360,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(1261,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ A @ C @ D ) @ ( c_Lambda_Osubstn @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ A @ C @ D ) @ ( c_Lambda_Osubstn @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(860,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(1378,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1019,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lem0_0) ).
thf(850,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(377,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(1299,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(175,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(839,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ B @ D ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(1352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ B @ D ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(158,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(803,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(1367,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(211,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(923,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(639,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ A ) @ B )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(1417,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ A ) @ B )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(935,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(755,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(676,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1493,plain,
$false,
inference(cvc4,[status(thm)],[1322,809,1337,1411,629,1024,1168,846,628,518,1110,645,892,479,1105,666,1295,977,1211,582,1005,1406,683,1068,1422,1073,873,1142,1173,878,440,655,1305,597,1078,1137,533,1164,715,1275,698,945,930,1342,747,898,1001,1127,782,841,973,1254,1287,570,619,1191,1059,542,1409,724,1330,1264,917,751,817,559,1147,881,1362,1100,1232,1013,770,924,789,1373,1040,623,646,937,574,821,485,834,602,687,956,866,988,507,527,1119,774,428,1201,920,678,661,761,810,714,1206,452,512,942,1047,798,1057,1163,1387,1091,1355,1217,561,693,429,1370,815,729,1238,1042,952,467,566,1032,1365,852,1178,1296,830,889,461,493,757,1195,551,710,1079,1027,1360,1089,874,1017,615,1328,1064,980,1425,1006,593,869,499,857,742,578,1270,1259,650,948,884,1160,1082,488,1182,642,1414,1214,590,547,1419,1292,933,554,753,901,686,1075,476,1039,970,837,1114,1263,701,515,1382,1266,1131,1050,1246,779,984,911,605,1393,1318,1086,1241,633,1170,1035,1187,1167,530,794,926,765,1054,662,718,906,430,1103,824,1301,689,444,733,965,750,1154,819,975,1125,772,826,1226,958,1403,1139,1312,1107,1332,804,1224,764,1194,1209,1282,784,1011,1048,1349,996,1144,737,1122,509,434,599,1376,863,1175,631,1339,609,848,1325,895,1149,1344,1022,668,1112,626,915,932,1061,636,1066,1015,986,563,1250,505,658,912,521,1198,1396,455,883,473,722,1034,490,680,1277,812,1081,617,939,553,458,1134,648,776,580,1070,705,887,739,1098,993,712,557,1003,1400,707,954,1252,673,791,1186,441,585,502,1235,1285,1220,544,470,576,1358,744,1257,703,1052,727,1094,876,991,1372,595,1272,612,1180,539,482,671,1157,903,524,759,1189,1390,1316,450,1084,1289,844,588,961,963,652,1244,731,786,1030,1308,1077,899,832,1309,549,536,1045,1116,447,1280,432,967,1229,1248,735,999,620,950,1097,854,1303,1314,807,767,664,828,696,720,1346,796,928,918,801,437,1335,1129,1261,1268,1152,860,1384,1378,1019,908,850,982,1299,607,624,839,1352,464,803,1320,1367,923,1184,1037,639,1204,496,708,1417,935,1009,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL754-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 16:29:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.86/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.08 % [INFO] Parsing done (242ms).
% 1.78/1.09 % [INFO] Running in sequential loop mode.
% 2.44/1.40 % [INFO] eprover registered as external prover.
% 2.44/1.40 % [INFO] cvc4 registered as external prover.
% 2.44/1.41 % [INFO] Scanning for conjecture ...
% 2.92/1.56 % [INFO] Found a conjecture and 715 axioms. Running axiom selection ...
% 3.42/1.74 % [INFO] Axiom selection finished. Selected 424 axioms (removed 291 axioms).
% 3.97/1.89 % [INFO] Problem is propositional (TPTP CNF).
% 3.97/1.91 % [INFO] Type checking passed.
% 3.97/1.91 % [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 ...
% 12.53/3.81 % External prover 'cvc4' found a proof!
% 12.53/3.82 % [INFO] Killing All external provers ...
% 12.53/3.82 % Time passed: 3317ms (effective reasoning time: 2727ms)
% 12.53/3.82 % 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)>
% 12.53/3.82 % Axioms used in derivation (424): cls_Suc__pred_0, cls_not__one__less__zero_0, cls_less__iff__diff__less__0_0, cls_add__0__left_0, cls_add__Suc__shift_0, cls_add__pos__nonneg_0, cls_subst__lt_0, cls_power__0_0, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_add__is__1_1, cls_less__diff__iff_1, cls_zero__less__one_0, cls_lift_Osimps_I2_J_0, cls_add__less__cancel__left_1, cls_Suc__inject_0, cls_eq__imp__le_0, cls_subst__App_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_le__diff__iff_0, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_subst__eq_0, cls_le__diff__conv_1, cls_liftn_Osimps_I1_J_1, cls_beta__cases_I2_J_1, cls_dB_Osimps_I8_J_0, cls_one__is__add_4, cls_Suc__n__not__n_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_zero__le__one_0, cls_diff__Suc__1_0, cls_nat__add__left__cancel__less_1, cls_termination__basic__simps_I5_J_0, cls_add__increasing2_0, cls_eq__diff__iff_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_add__strict__right__mono_0, cls_less__antisym_0, cls_liftn_Osimps_I2_J_0, cls_power__increasing_0, cls_less__add__Suc2_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_add__le__cancel__left_1, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_less__Suc__eq_2, cls_not__less__eq_1, cls_nat__add__left__cancel__less_0, cls_one__is__add_1, cls_add__le__cancel__right_1, cls_appR_0, cls_termination__basic__simps_I1_J_0, cls_substn__subst__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_comm__monoid__add_Omult__1__right_0, cls_add__leE_0, cls_add__diff__assoc2_0, cls_comm__monoid__add_Omult__assoc_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_substn_Osimps_I1_J_2, cls_add__cancel__21_1, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_power__less__imp__less__exp_0, cls_lift__subst__lt_0, cls_power__le__imp__le__exp_0, cls_power__gt1_0, cls_add__nonpos__neg_0, cls_beta_0, cls_le__0__eq_0, cls_gr0I_0, cls_dB_Osimps_I7_J_0, cls_subst__preserves__beta_0, cls_add__gr__0_0, cls_add__nonneg__pos_0, cls_lem0_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_diff__diff__right_0, cls_diff__diff__left_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_class__semiring_Omul__0_0, cls_one__le__power_0, cls_gr__implies__not0_0, cls_add__le__mono_0, cls_diff__diff__cancel_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_le__antisym_0, cls_add__less__mono_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_diff__le__mono2_0, cls_Suc__le__mono_0, cls_mod__if_1, cls_less__iff__diff__less__0_1, cls_subst__gt_0, cls_double__eq__0__iff_1, cls_right__minus__eq_0, cls_substn__subst__n_0, cls_class__semiring_Omul__c_0, cls_liftn__0_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_class__semiring_Osemiring__rules_I12_J_0, cls_Suc__leI_0, cls_add__Suc_0, cls_subst__Var_2, cls_le__imp__diff__is__add_1, cls_dB_Osimps_I3_J_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_diff__add__inverse2_0, cls_add__nonneg__eq__0__iff_0, cls_add__less__cancel__right_1, cls_nat__add__left__commute_0, cls_trans__le__add2_0, cls_lift__lift_0, cls_one__is__add_5, cls_power__gt1__lemma_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_diff__Suc__Suc_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_class__semiring_Osemiring__rules_I2_J_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_beta__cases_I2_J_0, cls_last__upt_0, cls_add__strict__left__mono_0, cls_mod__le__divisor_0, cls_not__less__eq__eq_1, cls_le__iff__diff__le__0_0, cls_Suc__diff__1_0, cls_mod__Suc_0, cls_add__le__less__mono_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_combine__common__factor_0, cls_dB_Osimps_I4_J_0, cls_add__is__1_0, cls_class__semiring_Oadd__a_0, cls_one__is__add_0, cls_less__add__Suc1_0, cls_trans__le__add1_0, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__mono1_0, cls_less__Suc__eq__le_1, cls_le__mod__geq_0, cls_liftn_Osimps_I3_J_0, cls_termination__basic__simps_I4_J_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_class__semiring_Osemiring__rules_I19_J_0, cls_termination__basic__simps_I3_J_0, cls_class__semiring_Osemiring__rules_I17_J_0, cls_power__less__power__Suc_0, cls_comm__monoid__add_Omult__commute_0, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_nat__add__assoc_0, cls_power__strict__mono_0, cls_One__nat__def_0, cls_less__add__one_0, cls_add__strict__mono_0, cls_lessI_0, cls_Suc__le__mono_1, cls_diff__Suc__eq__diff__pred_0, cls_zero__less__two_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_le__SucE_0, cls_power__strict__decreasing_0, cls_zero__less__power_0, cls_add__cancel__21_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_less__Suc__eq__0__disj_3, cls_less__add__eq__less_0, cls_diff__Suc__diff__eq1_0, cls_class__semiring_Omul__d_0, cls_lift_Osimps_I3_J_0, cls_dB_Osimps_I1_J_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_subst__Var_1, cls_power__Suc_0, cls_diff__Suc__diff__eq2_0, cls_diff__less_0, cls_zero__neq__one_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_diff__self_0, cls_less__imp__diff__less_0, cls_diff__is__0__eq_0, cls_natgb_Oadd__cancel_0, cls_mod__Suc_1, cls_neq0__conv_1, cls_less__1__mult_0, cls_one__is__add_2, cls_add__less__cancel__right_0, cls_add__diff__cancel_0, cls_le__trans_0, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_add__Suc__right_0, cls_class__semiring_Osemiring__rules_I28_J_0, cls_class__semiring_Omul__a_0, cls_add__diff__assoc_0, cls_diff__add__assoc_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_substn_Osimps_I1_J_0, cls_le__imp__diff__is__add_0, cls_Suc__le__eq_0, cls_class__semiring_Omul__1_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, cls_mod__1_0, cls_less__not__refl_0, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_linorder__neqE__ordered__idom_0, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_gr0__conv__Suc_1, cls_add__nonneg__eq__0__iff_1, cls_class__semiring_Osemiring__rules_I3_J_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_lift__subst_0, cls_diff__less__Suc_0, cls_right__minus__eq_1, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_dB_Osimps_I2_J_1, cls_add__nonneg__nonneg_0, clsarity_nat__Ring__and__Field_Osemiring, cls_less__diff__conv_1, cls_le__diff__conv2_0, cls_less__diff__conv_0, cls_nat_Oinject_0, cls_add__lessD1_0, cls_diff__less__mono_0, cls_even__less__0__iff_1, cls_less__SucE_0, cls_subst__subst_0, cls_power__eq__imp__eq__base_0, cls_le__diff__conv_0, cls_mult__strict__left__mono__comm_0, cls_add__strict__increasing_0, cls_power__strict__increasing__iff_1, cls_power__le__imp__le__base_0, cls_nat__add__left__cancel__le_1, cls_le__add__diff__inverse_0, cls_less__eq__Suc__le_0, cls_substn_Osimps_I2_J_0, cls_not__less__less__Suc__eq_1, cls_class__semiring_Opwr__Suc_0, clsarity_nat__Power_Opower, cls_power__increasing__iff_1, cls_Nat_Oadd__0__right_0, cls_class__semiring_Osemiring__rules_I11_J_0, cls_liftn__lift_0, cls_eq__eqI_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_lift_Osimps_I1_J_1, cls_Suc__lessD_0, cls_nat__neq__iff_0, cls_le__less__Suc__eq_0, cls_le0_0, cls_natgb_Oadd__r0__iff_0, cls_less__eq__Suc__le_1, cls_add__is__1_4, cls_le__eqI_0, cls_add__is__1_5, cls_diff__self__eq__0_0, cls_le__add2_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_less__Suc__eq__le_0, cls_add__neg__neg_0, cls_mod__less__eq__dividend_0, cls_add__eq__if_1, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_nat__add__left__cancel__le_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_abs_0, cls_less__Suc0_0, cls_comm__monoid__add_Omult__left__commute_0, cls_diff__0__right_0, cls_le__add__right__mono_0, cls_diff__Suc__less_0, cls_diff__le__self_0, cls_nat__less__le_0, cls_lift__IT_0, cls_le__diff__conv2_1, cls_nat_Osimps_I3_J_0, cls_less__trans__Suc_0, cls_le__Suc__eq_2, cls_plus__nat_Oadd__0_0, cls_nat__less__le_2, clsarity_nat__Ring__and__Field_Omult__mono1, cls_diff__add__assoc2_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_diff__less__mono2_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_trans__less__add1_0, cls_class__semiring_Osemiring__rules_I35_J_0, cls_comm__monoid__add_Omult__1_0, cls_liftn_Osimps_I1_J_0, cls_add__nonneg__eq__0__iff_2, cls_add__is__0_2, cls_eq__eqI_1, cls_less__diff__iff_0, cls_zero__less__diff_1, cls_one__less__power_0, cls_power__Suc__less__one_0, cls_add__le__mono1_0, cls_minus__nat_Odiff__0_0, cls_add__is__1_3, cls_le__iff__add_1, cls_class__semiring_Osemiring__rules_I27_J_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_Suc__n__not__le__n_0, cls_class__semiring_Oadd__c_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_Suc__leD_0, cls_substn_Osimps_I1_J_1, cls_add__eq__self__zero_0, cls_le__diff__iff_1, cls_add__pos__pos_0, cls_power__less__imp__less__base_0, cls_mod__less__divisor_0, cls_Suc__eq__plus1_0, cls_n__not__Suc__n_0, cls_power__inject__base_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_less__SucI_0, cls_add__neg__nonpos_0, cls_beta__cases_I1_J_0, cls_not__less0_0, cls_dB_Osimps_I2_J_0, cls_substn_Osimps_I3_J_0, cls_diffs0__imp__equal_0, cls_class__semiring_Opwr__mul_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_eq__iff__diff__eq__0_1, cls_subst__Abs_0, cls_add__less__cancel__left_0, cls_one__is__add_3, cls_dB_Osimps_I5_J_0, cls_diff__add__inverse_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_Suc__less__eq_0, cls_le__iff__diff__le__0_1, cls_lift_Osimps_I1_J_0, cls_zero__le__power_0, cls_power__increasing__iff_0, cls_add__leE_1, cls_Suc__pred_H_0, cls_subst__Var_0, cls_le__eqI_1, cls_Lambda_0, cls_class__semiring_Opwr__0_0, cls_Suc__diff__le_0, cls_add__gr__0_2, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_monoid__add__class_Oadd__0__right_0, cls_add__gr__0_1, cls_diff__commute_0, cls_le__add1_0, cls_power__strict__increasing__iff_0, cls_mod__if_0, cls_le__less__Suc__eq_1, cls_less__Suc0_1, cls_subst__lift_0, cls_termination__basic__simps_I2_J_0, cls_le__eq__less__or__eq_0, cls_class__semiring_Omul__pwr_0, cls_eq__iff__diff__eq__0_0, cls_add__strict__increasing2_0, cls_le__add__diff_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, cls_appL_0, cls_nat__less__le_1, cls_add__le__cancel__left_0, cls_power__Suc__less_0, cls_power__decreasing_0, cls_less__eqI_1, cls_dB_Osimps_I9_J_0, cls_zero__less__Suc_0, cls_class__semiring_Osemiring__rules_I4_J_0, cls_le__neq__implies__less_0, cls_not__one__le__zero_0, cls_le__refl_0, cls_not__less__eq__eq_0, cls_mod__Suc__eq__Suc__mod_0, cls_add__le__cancel__right_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_add__diff__inverse_0, cls_power__mono_0, cls_even__less__0__iff_0, cls_le__SucI_0
% 12.53/3.82 % No. of inferences in proof: 855
% 12.53/3.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3317 ms resp. 2727 ms w/o parsing
% 13.44/4.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.44/4.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------