%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:52:43 AM UTC 2026
% Result : Unsatisfiable 100.31s 22.17s
% Output : Refutation 100.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 431
% Syntax : Number of formulae : 1449 ( 437 unt; 0 typ; 4 def)
% Number of atoms : 3413 (1249 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 16856 (1818 ~;1580 |; 0 &;13458 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 6 con; 0-3 aty)
% Number of variables : 3193 ( 0 ^;3185 !; 4 ?;3193 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_InductTermi_OIT_decl,type,
c_InductTermi_OIT: $i > $o ).
thf(v_ra_decl,type,
v_ra: $i ).
thf(c_Lambda_Osubst_decl,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(c_Lambda_OdB_OVar_decl,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(c_Lambda_OdB_OAbs_decl,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(v_ia_decl,type,
v_ia: $i ).
thf(v_ja_decl,type,
v_ja: $i ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Lambda_Olift_decl,type,
c_Lambda_Olift: $i > $i > $i ).
thf(c_Lambda_OdB_OApp_decl,type,
c_Lambda_OdB_OApp: $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_Lambda_Oliftn_decl,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(class_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Lambda_Obeta_decl,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(c_Lambda_Osubstn_decl,type,
c_Lambda_Osubstn: $i > $i > $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(c_List_Oupt_decl,type,
c_List_Oupt: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Lambda_Osko__Lambda__Xbeta__cases__2__1_decl,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Lambda_OdB_OVar @ A )
= B ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Lambda_OdB_OAbs @ A )
= B ) ) ) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(892,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(228,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(961,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(962,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(cnf,[status(esa)],[961]) ).
thf(963,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[962]) ).
thf(1,negated_conjecture,
v_ra @ c_InductTermi_OIT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(428,plain,
v_ra @ c_InductTermi_OIT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,negated_conjecture,
~ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(430,plain,
~ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(431,plain,
~ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ),
inference(polarity_switch,[status(thm)],[430]) ).
thf(1433,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[428,431]) ).
thf(1434,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1433]) ).
thf(1435,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= v_ra ),
inference(simp,[status(thm)],[1434]) ).
thf(3665,plain,
! [A: $i] :
( ( A
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,1435]) ).
thf(3666,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3665:[bind(A,$thf( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ))]]) ).
thf(253,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(1018,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1019,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(polarity_switch,[status(thm)],[1018]) ).
thf(4160,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(paramod_ordered,[status(thm)],[3666,1019]) ).
thf(4161,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(simp,[status(thm)],[4160]) ).
thf(4165,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= A )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= A )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(simp,[status(thm)],[4161]) ).
thf(4170,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(simp,[status(thm)],[4165]) ).
thf(4186,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A != v_ra )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,4170]) ).
thf(4187,plain,
! [A: $i] :
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A != v_ra )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[4186:[]]) ).
thf(4188,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( v_ra @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[4187]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(80,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(629,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(237,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(983,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(984,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(polarity_switch,[status(thm)],[983]) ).
thf(4148,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(paramod_ordered,[status(thm)],[3666,984]) ).
thf(4149,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(simp,[status(thm)],[4148]) ).
thf(4164,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(simp,[status(thm)],[4149]) ).
thf(4169,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= v_ra ) ),
inference(simp,[status(thm)],[4164]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(177,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(846,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(394,axiom,
! [A: $i] :
( ~ ( A @ c_InductTermi_OIT )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(1341,plain,
! [A: $i] :
( ~ ( A @ c_InductTermi_OIT )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1342,plain,
! [A: $i] :
( ~ ( A @ c_InductTermi_OIT )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(cnf,[status(esa)],[1341]) ).
thf(1838,plain,
! [A: $i] :
( ( ( v_ra @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[428,1342]) ).
thf(1839,plain,
! [A: $i] :
( ( ( v_ra @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1840,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[1839:[bind(A,$thf( v_ra ))]]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(518,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
inference(cnf,[status(esa)],[479]) ).
thf(481,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Power_Opower )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[480]) ).
thf(1846,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[1840,1342]) ).
thf(1847,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1846]) ).
thf(1848,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[1847:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs ))]]) ).
thf(3676,plain,
! [A: $i] :
( ( A
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,431]) ).
thf(3677,plain,
( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3676:[bind(A,$thf( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ))]]) ).
thf(4304,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3677,1019]) ).
thf(4305,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[4304]) ).
thf(4313,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= A )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= A )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[4305]) ).
thf(4339,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[4313]) ).
thf(4474,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1848,4339]) ).
thf(4475,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4474]) ).
thf(4481,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4475]) ).
thf(5086,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,4481]) ).
thf(5087,plain,
! [A: $i] :
( ( A
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[5086:[]]) ).
thf(5088,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5087]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(1369,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(331,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(1190,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(2040,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[1848,1342]) ).
thf(2041,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2040]) ).
thf(2042,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2041:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2046,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2042,1342]) ).
thf(2047,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2046]) ).
thf(2048,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2047:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2052,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2048,1342]) ).
thf(2053,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2052]) ).
thf(2054,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2053:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2058,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2054,1342]) ).
thf(2059,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2058]) ).
thf(2060,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2059:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2064,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2060,1342]) ).
thf(2065,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2064]) ).
thf(2066,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2065:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2077,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2066,1342]) ).
thf(2078,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2077]) ).
thf(2079,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2078:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2083,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2079,1342]) ).
thf(2084,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2083]) ).
thf(2085,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2084:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2103,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2085,1342]) ).
thf(2104,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2103]) ).
thf(2105,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2104:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2334,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2105,1342]) ).
thf(2335,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2334]) ).
thf(2336,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2335:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] : ( B @ ( A @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(429,plain,
! [B: $i,A: $i] : ( B @ ( A @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[429,431]) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1436]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) ),
inference(simp,[status(thm)],[1437]) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( B != v_ja )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( v_ia @ c_Lambda_OdB_OVar ) )
| ( ( v_ra @ c_Lambda_OdB_OAbs )
!= v_ra ) ),
inference(simp,[status(thm)],[1438]) ).
thf(1452,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OVar )
!= ( v_ia @ c_Lambda_OdB_OVar ) )
| ( ( v_ra @ c_Lambda_OdB_OAbs )
!= v_ra ) ),
inference(simp,[status(thm)],[1451]) ).
thf(1453,plain,
! [A: $i] :
( ( A != v_ia )
| ( ( v_ra @ c_Lambda_OdB_OAbs )
!= v_ra ) ),
inference(simp,[status(thm)],[1452]) ).
thf(1454,plain,
( ( v_ra @ c_Lambda_OdB_OAbs )
!= v_ra ),
inference(simp,[status(thm)],[1453]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(909,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[429,1342]) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1835]) ).
thf(1837,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(pattern_uni,[status(thm)],[1836:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) ))]]) ).
thf(1845,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(simp,[status(thm)],[1837]) ).
thf(3731,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,1845]) ).
thf(3732,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3731:[bind(A,$thf( F @ ( G @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) )),bind(B,$thf( F )),bind(C,$thf( G ))]]) ).
thf(3979,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[3732]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[521]) ).
thf(523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[522]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
| ( A
= ( A @ ( B @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
| ( A
= ( A @ ( B @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[461]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[462]) ).
thf(240,axiom,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(989,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(990,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(lifteq,[status(thm)],[989]) ).
thf(188,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(876,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(280,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(1076,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1077,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_Suc ) ),
inference(lifteq,[status(thm)],[1076]) ).
thf(3177,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1077,984]) ).
thf(3178,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ),
inference(pattern_uni,[status(thm)],[3177:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ c_HOL_Oone__class_Oone )),bind(C,$thf( A ))]]) ).
thf(9086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[876,3178]) ).
thf(9087,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9086]) ).
thf(9116,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= C )
| ( A
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[9087]) ).
thf(9129,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= B ),
inference(simp,[status(thm)],[9116]) ).
thf(10939,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone )
!= B ) ),
inference(paramod_ordered,[status(thm)],[990,9129]) ).
thf(10961,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[10939]) ).
thf(11382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(paramod_ordered,[status(thm)],[463,10961]) ).
thf(11383,plain,
( ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(pattern_uni,[status(thm)],[11382:[bind(A,$thf( tc_nat )),bind(B,$thf( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc )),bind(C,$thf( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc ))]]) ).
thf(20450,plain,
( ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ $true ),
inference(rewrite,[status(thm)],[11383,629,1077]) ).
thf(20451,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[20450]) ).
thf(20507,plain,
! [A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,20451]) ).
thf(20508,plain,
! [A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20507]) ).
thf(20509,plain,
tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(pattern_uni,[status(thm)],[20508:[bind(A,$thf( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ))]]) ).
thf(20671,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( A @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20509,3178]) ).
thf(20672,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( A @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20671]) ).
thf(20732,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
!= A )
| ( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[20672]) ).
thf(20798,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[20732]) ).
thf(208,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(920,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(3159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[920,984]) ).
thf(3160,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[3159]) ).
thf(3182,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[3160]) ).
thf(3188,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[3182]) ).
thf(4386,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,3188]) ).
thf(4387,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[4386]) ).
thf(4388,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(pattern_uni,[status(thm)],[4387:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_HOL_Oplus__class_Oplus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(4410,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[4388]) ).
thf(5493,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4410,3178]) ).
thf(5494,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5493]) ).
thf(5520,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ( ( C @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[5494]) ).
thf(5536,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[5520]) ).
thf(5636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ c_Suc @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[1077,5536]) ).
thf(5637,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(pattern_uni,[status(thm)],[5636:[bind(A,$thf( E @ c_Suc )),bind(B,$thf( tc_nat @ c_HOL_Oone__class_Oone )),bind(C,$thf( E ))]]) ).
thf(5644,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[5637]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(994,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(1401,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(1053,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1054,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_Suc ) ),
inference(lifteq,[status(thm)],[1053]) ).
thf(211,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(926,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(2946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( tc_nat @ ( A @ c_Suc @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1054,926]) ).
thf(2947,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2946:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( tc_nat @ c_HOL_Oone__class_Oone ))]]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(690,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(691,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(cnf,[status(esa)],[690]) ).
thf(692,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(lifteq,[status(thm)],[691]) ).
thf(693,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ),
inference(detectInverse,[status(thm)],[692]) ).
thf(694,plain,
! [A: $i] :
( ( A @ c_Suc @ sk2 )
= A ),
inference(cnf,[status(esa)],[693]) ).
thf(1726,plain,
! [A: $i] :
( ( A @ c_Suc @ sk2 )
= A ),
inference(lifteq,[status(thm)],[694]) ).
thf(1727,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone @ sk2 )
= A ) ),
inference(paramod_ordered,[status(thm)],[990,1726]) ).
thf(1728,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ sk2 )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(pattern_uni,[status(thm)],[1727:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero ))]]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[447]) ).
thf(449,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[448]) ).
thf(7,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(440,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(677,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(1305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(3728,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,1845]) ).
thf(3729,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3728:[bind(A,$thf( G @ ( H @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs )),bind(B,$thf( G )),bind(C,$thf( H ))]]) ).
thf(3977,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[3729]) ).
thf(10244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3977,1019]) ).
thf(10245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[10244]) ).
thf(10251,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs )
!= C )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[10245]) ).
thf(10262,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[10251]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(741,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(279,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1073,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(2070,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[1845,1342]) ).
thf(2071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2070]) ).
thf(2072,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(pattern_uni,[status(thm)],[2071:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G @ ( H @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs ))]]) ).
thf(2076,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(simp,[status(thm)],[2072]) ).
thf(2112,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2076,431]) ).
thf(2113,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2112]) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) ),
inference(simp,[status(thm)],[2113]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1142,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(281,axiom,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1078,plain,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(175,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(841,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(842,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(polarity_switch,[status(thm)],[841]) ).
thf(9063,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[876,842]) ).
thf(9064,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9063]) ).
thf(9114,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A != C ) ),
inference(simp,[status(thm)],[9064]) ).
thf(9127,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[9114]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[549]) ).
thf(4200,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[920,3178]) ).
thf(4201,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[4200]) ).
thf(4212,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( ( B @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4201]) ).
thf(4220,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[4212]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[470]) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[471]) ).
thf(347,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).
thf(814,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(11005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3979,842]) ).
thf(11006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[11005]) ).
thf(11045,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[11006]) ).
thf(11055,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[11045]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[536]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[537]) ).
thf(205,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(914,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(19151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[914,1019]) ).
thf(19152,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[19151]) ).
thf(19159,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= C )
| ( A != C ) ),
inference(simp,[status(thm)],[19152]) ).
thf(19180,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= B ),
inference(simp,[status(thm)],[19159]) ).
thf(9078,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1054,876]) ).
thf(9079,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ),
inference(pattern_uni,[status(thm)],[9078:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ c_HOL_Oone__class_Oone )),bind(C,$thf( A ))]]) ).
thf(9194,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9079,3178]) ).
thf(9195,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9194]) ).
thf(9213,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc @ c_Suc )
!= B )
| ( ( B @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(simp,[status(thm)],[9195]) ).
thf(9233,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[9213]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(945,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(372,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(1291,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(1292,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(polarity_switch,[status(thm)],[1291]) ).
thf(7384,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ra @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[4188,1292]) ).
thf(7385,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ra @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[7384]) ).
thf(7435,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != v_ra )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[7385]) ).
thf(7452,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( v_ra @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[7435]) ).
thf(169,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(828,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(829,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[828]) ).
thf(198,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(898,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(2954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( tc_nat @ ( A @ c_Suc @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1077,926]) ).
thf(2955,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[2954:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ c_HOL_Oone__class_Oone )),bind(C,$thf( A ))]]) ).
thf(128,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(737,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(738,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[737]) ).
thf(2965,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2955,738]) ).
thf(2966,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2965]) ).
thf(2970,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( ( B @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(simp,[status(thm)],[2966]) ).
thf(2972,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[2970]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
inference(polarity_switch,[status(thm)],[1389]) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
inference(lifteq,[status(thm)],[1390]) ).
thf(114,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(709,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( B @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(1359,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(2080,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2066,431]) ).
thf(2081,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2080]) ).
thf(2082,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2081]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(1366,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[434]) ).
thf(436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[435]) ).
thf(360,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(1265,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(1254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(3216,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,429]) ).
thf(3217,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3216:[bind(A,$thf( F @ ( G @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) )),bind(B,$thf( G )),bind(C,$thf( F ))]]) ).
thf(3976,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[3217]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[554]) ).
thf(556,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B ) ),
inference(lifteq,[status(thm)],[555]) ).
thf(20286,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ~ $true
| ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[629,556]) ).
thf(20287,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B ) ),
inference(simp,[status(thm)],[20286]) ).
thf(20288,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower ) ) )
= A ),
inference(pattern_uni,[status(thm)],[20287:[bind(A,$thf( tc_nat ))]]) ).
thf(20340,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower ) ) )
= A ),
inference(simp,[status(thm)],[20288]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(502,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[502]) ).
thf(504,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B ) ),
inference(lifteq,[status(thm)],[503]) ).
thf(1323,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
= A ),
inference(lifteq,[status(thm)],[1322]) ).
thf(1191,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[1190]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(1132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(724,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(1313,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(cnf,[status(esa)],[458]) ).
thf(460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[459]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(559,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(1377,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
inference(polarity_switch,[status(thm)],[1377]) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
inference(lifteq,[status(thm)],[1378]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_Olift ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_Olift ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(312,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( D @ ( B @ ( E @ c_Lambda_Osubst ) ) @ ( D @ c_Suc @ ( C @ ( B @ c_Lambda_Olift ) @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Osubst ) ) )
= ( D @ ( B @ ( C @ ( E @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Osubst ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(1147,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( D @ ( B @ ( E @ c_Lambda_Osubst ) ) @ ( D @ c_Suc @ ( C @ ( B @ c_Lambda_Olift ) @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Osubst ) ) )
= ( D @ ( B @ ( C @ ( E @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Osubst ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1608,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[990,738]) ).
thf(1609,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1608:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero ))]]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_Oliftn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_Oliftn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(292,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(1100,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(606,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(285,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1084,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(3173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1084,984]) ).
thf(3174,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[3173]) ).
thf(3183,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= C )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(simp,[status(thm)],[3174]) ).
thf(3189,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= B ),
inference(simp,[status(thm)],[3183]) ).
thf(5048,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= C )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,3189]) ).
thf(5049,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= B )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[5048:[bind(A,$thf( tc_nat @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(5072,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[5049]) ).
thf(5323,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(rewrite,[status(thm)],[5072,990]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(1398,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(881,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(421,axiom,
! [B: $i,A: $i] :
~ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Obeta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(1415,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Obeta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(5662,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[990,5644]) ).
thf(5663,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(pattern_uni,[status(thm)],[5662:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero ))]]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(cnf,[status(esa)],[441]) ).
thf(443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Osemiring )
| ( ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(lifteq,[status(thm)],[442]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2076,1342]) ).
thf(2110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2109]) ).
thf(2111,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(pattern_uni,[status(thm)],[2110:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( H @ ( I @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2115,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(simp,[status(thm)],[2111]) ).
thf(2116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2115,1342]) ).
thf(2117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2116]) ).
thf(2118,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(pattern_uni,[status(thm)],[2117:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( I @ ( J @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2122,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(simp,[status(thm)],[2118]) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
inference(cnf,[status(esa)],[1401]) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
inference(lifteq,[status(thm)],[1402]) ).
thf(1404,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Lambda_OdB_OAbs @ A )
= B ),
inference(detectInverse,[status(thm)],[1403]) ).
thf(1405,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs @ sk6 )
= A ),
inference(cnf,[status(esa)],[1404]) ).
thf(1828,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs @ sk6 )
= A ),
inference(lifteq,[status(thm)],[1405]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[512]) ).
thf(514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[513]) ).
thf(254,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(1020,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(806,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(1183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(1334,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(87,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(646,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(834,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(1051,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(141,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(766,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1841,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) )
| ~ $true
| ~ ( A @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[1342,431]) ).
thf(1842,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1841]) ).
thf(1843,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1842]) ).
thf(105,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(687,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(634,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(3219,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ c_Lambda_OdB_OVar ) )
| ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,429]) ).
thf(3220,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
| ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3219:[bind(A,$thf( D @ c_Lambda_OdB_OVar )),bind(B,$thf( D ))]]) ).
thf(3978,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
| ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[3220]) ).
thf(5712,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3978,842]) ).
thf(5713,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[5712]) ).
thf(5747,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( B @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C )
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[5713]) ).
thf(5760,plain,
! [B: $i,A: $i] :
( ( ( B @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[5747]) ).
thf(5788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( B @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[5760,1342]) ).
thf(5789,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( B @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[5788]) ).
thf(5790,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(pattern_uni,[status(thm)],[5789:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) ))]]) ).
thf(5812,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[5790]) ).
thf(6747,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[5812,1342]) ).
thf(6748,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[6747]) ).
thf(6749,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(pattern_uni,[status(thm)],[6748:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs ))]]) ).
thf(6772,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[6749]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(527,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4460,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2054,4339]) ).
thf(4461,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4460]) ).
thf(4483,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4461]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(774,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(336,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(452,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[3978,1342]) ).
thf(5704,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5703]) ).
thf(5705,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[5704:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) ))]]) ).
thf(5751,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5705]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(1067,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(117,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(714,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(4144,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A != v_ra )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,3666]) ).
thf(4145,plain,
! [A: $i] :
( ( A != v_ra )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[4144:[]]) ).
thf(4172,plain,
( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( v_ra @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[4145]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(438,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[437]) ).
thf(439,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B ) ),
inference(lifteq,[status(thm)],[438]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(cnf,[status(esa)],[544]) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( C = B ) ),
inference(lifteq,[status(thm)],[545]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(793,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
inference(polarity_switch,[status(thm)],[1336]) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
inference(lifteq,[status(thm)],[1337]) ).
thf(1849,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1840,431]) ).
thf(1850,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1849]) ).
thf(1851,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[1850]) ).
thf(3479,plain,
! [A: $i] :
( ( A
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,1851]) ).
thf(3480,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs ) )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3479:[bind(A,$thf( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ))]]) ).
thf(5108,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( v_ra @ c_Lambda_OdB_OAbs ) )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,3480]) ).
thf(5109,plain,
! [A: $i] :
( ( A
!= ( v_ra @ c_Lambda_OdB_OAbs ) )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[5108:[]]) ).
thf(5142,plain,
( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( v_ra @ c_Lambda_OdB_OAbs @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5109]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1163,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1274,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubst ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubst ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OApp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubst ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubst ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OApp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(778,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(264,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(1042,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(630,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(788,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(729,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(1223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(342,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1217,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(598,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Olift ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Olift ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(3163,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1054,984]) ).
thf(3164,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ),
inference(pattern_uni,[status(thm)],[3163:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( tc_nat @ c_HOL_Oone__class_Oone ))]]) ).
thf(9110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[876,3164]) ).
thf(9111,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9110]) ).
thf(9119,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( A
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[9111]) ).
thf(9132,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[9119]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1027,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(757,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(1012,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem0_0) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(2352,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( B @ c_InductTermi_OIT ) )
| ( ( B @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ $true
| ~ ( A @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[1342,1843]) ).
thf(2353,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( B @ c_InductTermi_OIT ) )
| ( ( B @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2352]) ).
thf(2354,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(pattern_uni,[status(thm)],[2353:[bind(A,$thf( C )),bind(B,$thf( C @ c_Lambda_OdB_OAbs ))]]) ).
thf(2391,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2354]) ).
thf(2619,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( B @ c_InductTermi_OIT ) )
| ( ( B @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ $true
| ~ ( A @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[1342,2391]) ).
thf(2620,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( B @ c_InductTermi_OIT ) )
| ( ( B @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2619]) ).
thf(2621,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(pattern_uni,[status(thm)],[2620:[bind(A,$thf( C )),bind(B,$thf( C @ c_Lambda_OdB_OAbs ))]]) ).
thf(2663,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2621]) ).
thf(7394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[920,1292]) ).
thf(7395,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7394]) ).
thf(7440,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[7395]) ).
thf(7457,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[7440]) ).
thf(7472,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,7457]) ).
thf(7473,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7472]) ).
thf(7474,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(pattern_uni,[status(thm)],[7473:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(7503,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[7474]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(1296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(665,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(583,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(830,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_0) ).
thf(1392,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(9108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1077,876]) ).
thf(9109,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(pattern_uni,[status(thm)],[9108:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( tc_nat @ c_HOL_Oone__class_Oone ))]]) ).
thf(9835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9109,1292]) ).
thf(9836,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9835]) ).
thf(9873,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc @ c_Suc )
!= B )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(simp,[status(thm)],[9836]) ).
thf(9884,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ c_Suc )
!= A ),
inference(simp,[status(thm)],[9873]) ).
thf(11570,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc )
!= A ) ),
inference(paramod_ordered,[status(thm)],[990,9884]) ).
thf(11594,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[11570]) ).
thf(11602,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[11594]) ).
thf(10960,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(simp,[status(thm)],[10939]) ).
thf(11420,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(rewrite,[status(thm)],[10960,990]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
thf(710,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(4434,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1840,4339]) ).
thf(4435,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4434]) ).
thf(4477,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4435]) ).
thf(4510,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( v_ra @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,4477]) ).
thf(4511,plain,
! [A: $i] :
( ( A
!= ( v_ra @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[4510:[]]) ).
thf(4512,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( v_ra @ c_Lambda_OdB_OAbs @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[4511]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(71,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(610,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(1270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(980,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(199,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(901,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1498,plain,
tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(rewrite,[status(thm)],[901,990]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(1082,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(cnf,[status(esa)],[524]) ).
thf(526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[525]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(cnf,[status(esa)],[488]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(2106,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2085,431]) ).
thf(2107,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2106]) ).
thf(2108,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2107]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Olift ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ ( B @ c_Lambda_Olift ) @ ( D @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(1329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Olift ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ ( B @ c_Lambda_Olift ) @ ( D @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(2869,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[766,1609]) ).
thf(2870,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2869]) ).
thf(2875,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(simp,[status(thm)],[2870]) ).
thf(2877,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[2875]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(933,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(753,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(252,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(1016,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(970,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubstn ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OApp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubstn ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OApp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(1324,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(985,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(1382,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(3005,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( B @ c_InductTermi_OIT ) )
| ( ( B @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ $true
| ~ ( A @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[1342,2663]) ).
thf(3006,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( B @ c_InductTermi_OIT ) )
| ( ( B @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[3005]) ).
thf(3007,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(pattern_uni,[status(thm)],[3006:[bind(A,$thf( C )),bind(B,$thf( C @ c_Lambda_OdB_OAbs ))]]) ).
thf(3059,plain,
! [A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ~ ( A @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[3007]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1192,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(245,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(1002,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(567,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(cnf,[status(esa)],[566]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(lifteq,[status(thm)],[567]) ).
thf(569,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ),
inference(detectInverse,[status(thm)],[568]) ).
thf(570,plain,
! [A: $i] :
( ( A @ c_Suc @ sk1 )
= A ),
inference(cnf,[status(esa)],[569]) ).
thf(1625,plain,
! [A: $i] :
( ( A @ c_Suc @ sk1 )
= A ),
inference(lifteq,[status(thm)],[570]) ).
thf(1626,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone @ sk1 )
= A ) ),
inference(paramod_ordered,[status(thm)],[990,1625]) ).
thf(1627,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ sk1 )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(pattern_uni,[status(thm)],[1626:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero ))]]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(647,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(268,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(1050,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(158,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(805,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(cnf,[status(esa)],[507]) ).
thf(209,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(921,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[539]) ).
thf(541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(lifteq,[status(thm)],[540]) ).
thf(320,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(1167,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(586,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(94,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(662,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(2055,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2048,431]) ).
thf(2056,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2055]) ).
thf(2057,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2056]) ).
thf(321,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1170,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(1286,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(260,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(1035,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(557,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(558,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(cnf,[status(esa)],[557]) ).
thf(278,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1071,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(2393,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2122,1342]) ).
thf(2394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2393]) ).
thf(2395,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(pattern_uni,[status(thm)],[2394:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( J @ ( K @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2402,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(simp,[status(thm)],[2395]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(1187,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(9183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9079,984]) ).
thf(9184,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9183]) ).
thf(9218,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc @ c_Suc )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(simp,[status(thm)],[9184]) ).
thf(9223,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[9218]) ).
thf(10656,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(paramod_ordered,[status(thm)],[990,9223]) ).
thf(10657,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(pattern_uni,[status(thm)],[10656:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero )),bind(B,$thf( B ))]]) ).
thf(10683,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[10657]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(856,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(444,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(19147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[914,3164]) ).
thf(19148,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[19147]) ).
thf(19157,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ( A
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[19148]) ).
thf(19178,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[19157]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(733,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(819,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(772,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(579,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(2983,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2947,1609]) ).
thf(2984,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2983]) ).
thf(2989,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(simp,[status(thm)],[2984]) ).
thf(2991,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[2989]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_Obeta ) )
| ( C @ ( A @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_Obeta ) )
| ( C @ ( A @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(176,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(843,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(1125,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(936,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(1371,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(381,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(1312,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(497,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[496]) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[497]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Lambda_Obeta ) )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Lambda_Obeta ) )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(7884,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7503,3178]) ).
thf(7885,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7884]) ).
thf(7904,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ( ( C @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[7885]) ).
thf(7924,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[7904]) ).
thf(7428,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3677,1292]) ).
thf(7429,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[7428]) ).
thf(7438,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[7429]) ).
thf(7455,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[7438]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Olift ) )
= ( C @ ( D @ ( B @ c_Lambda_Olift ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Olift ) )
= ( C @ ( D @ ( B @ c_Lambda_Olift ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(465,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[464]) ).
thf(466,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[465]) ).
thf(289,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(1092,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(333,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_List_Oupt ) @ c_List_Olast ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__upt_0) ).
thf(1194,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_List_Oupt ) @ c_List_Olast ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(519,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[518]) ).
thf(520,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[519]) ).
thf(9389,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ~ $true
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[629,520]) ).
thf(9390,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[9389]) ).
thf(9391,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(pattern_uni,[status(thm)],[9390:[bind(A,$thf( tc_nat ))]]) ).
thf(9560,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[9391]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1209,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(899,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(polarity_switch,[status(thm)],[898]) ).
thf(900,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[899]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Lambda_Obeta ) )
| ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Obeta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(1048,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Lambda_Obeta ) )
| ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Obeta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(2985,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2947,738]) ).
thf(2986,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2985]) ).
thf(2990,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( A
!= ( B @ c_Suc ) ) ),
inference(simp,[status(thm)],[2986]) ).
thf(2992,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc )
!= A ),
inference(simp,[status(thm)],[2990]) ).
thf(3101,plain,
! [A: $i] :
( ( ( A @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone )
!= A ) ),
inference(paramod_ordered,[status(thm)],[990,2992]) ).
thf(3104,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(simp,[status(thm)],[3101]) ).
thf(3106,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(rewrite,[status(thm)],[3104,990]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(cnf,[status(esa)],[450]) ).
thf(408,axiom,
! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(1376,plain,
! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(6777,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ~ $true
| ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[629,504]) ).
thf(6778,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B ) ),
inference(simp,[status(thm)],[6777]) ).
thf(6779,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
inference(pattern_uni,[status(thm)],[6778:[bind(A,$thf( tc_nat ))]]) ).
thf(6942,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
inference(simp,[status(thm)],[6779]) ).
thf(7901,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7503,1019]) ).
thf(7902,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7901]) ).
thf(7913,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C ) ),
inference(simp,[status(thm)],[7902]) ).
thf(7933,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[7913]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(784,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Lambda_Obeta ) )
| ( B @ ( C @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Lambda_Obeta ) )
| ( B @ ( C @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(996,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1491,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[990,900]) ).
thf(1492,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(pattern_uni,[status(thm)],[1491:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero ))]]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(649,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(379,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(1307,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(890,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(161,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(811,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(282,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1080,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(cnf,[status(esa)],[551]) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[533]) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[534]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(726,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(895,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(769,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(1293,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(319,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(1166,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(6641,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1166,738]) ).
thf(6642,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6641]) ).
thf(6657,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ( A
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[6642]) ).
thf(6660,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= B ),
inference(simp,[status(thm)],[6657]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(848,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(227,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(959,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(868,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6089,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1100,738]) ).
thf(6090,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6089]) ).
thf(6095,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[6090]) ).
thf(6100,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( B @ c_Suc ) ),
inference(simp,[status(thm)],[6095]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(922,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(lifteq,[status(thm)],[921]) ).
thf(2067,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2060,431]) ).
thf(2068,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2067]) ).
thf(2069,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2068]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1845,431]) ).
thf(2074,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2073]) ).
thf(2075,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs )
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) ),
inference(simp,[status(thm)],[2074]) ).
thf(2049,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2042,431]) ).
thf(2050,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2049]) ).
thf(2051,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2050]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(351,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1245,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_InductTermi_OIT )
| ( B @ ( A @ c_Lambda_Olift ) @ c_InductTermi_OIT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(1364,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_InductTermi_OIT )
| ( B @ ( A @ c_Lambda_Olift ) @ c_InductTermi_OIT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(9854,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9109,3178]) ).
thf(9855,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( B @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9854]) ).
thf(9871,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc @ c_Suc )
!= B )
| ( A
!= ( B @ c_Suc ) ) ),
inference(simp,[status(thm)],[9855]) ).
thf(9883,plain,
! [A: $i] :
( ( A @ c_Suc @ c_Suc @ c_Suc )
!= A ),
inference(simp,[status(thm)],[9871]) ).
thf(9893,plain,
! [A: $i] :
( ( ( A @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc )
!= A ) ),
inference(paramod_ordered,[status(thm)],[990,9883]) ).
thf(9902,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(simp,[status(thm)],[9893]) ).
thf(10186,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_Suc @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(rewrite,[status(thm)],[9902,990]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(377,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(1303,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(1304,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(lifteq,[status(thm)],[1303]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(589,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(2871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[766,738]) ).
thf(2872,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2871]) ).
thf(2876,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != C )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[2872]) ).
thf(2878,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( B @ c_Suc ) ),
inference(simp,[status(thm)],[2876]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(812,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(48,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(553,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(cnf,[status(esa)],[547]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[485]) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[486]) ).
thf(283,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(1081,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(749,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(3726,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ c_Lambda_OdB_OVar ) )
| ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,1845]) ).
thf(3727,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3726:[bind(A,$thf( D @ c_Lambda_OdB_OVar )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(3975,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[3727]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(2595,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2336,1342]) ).
thf(2596,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2595]) ).
thf(2597,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2596:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(19088,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[914,842]) ).
thf(19089,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[19088]) ).
thf(19161,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A != C ) ),
inference(simp,[status(thm)],[19089]) ).
thf(19182,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[19161]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(1181,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(2944,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[926,738]) ).
thf(2945,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2944]) ).
thf(2957,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ( A
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[2945]) ).
thf(2961,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= B ),
inference(simp,[status(thm)],[2957]) ).
thf(3904,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,2961]) ).
thf(3905,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= B )
| ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3904:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )),bind(B,$thf( E )),bind(C,$thf( G ))]]) ).
thf(4066,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[3905]) ).
thf(4812,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(rewrite,[status(thm)],[4066,990]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ c_Suc @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) )
= ( B @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ c_Suc @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) )
= ( B @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(776,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(887,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(7420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1084,1292]) ).
thf(7421,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7420]) ).
thf(7444,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(simp,[status(thm)],[7421]) ).
thf(7462,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= A ),
inference(simp,[status(thm)],[7444]) ).
thf(361,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1267,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(346,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1230,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(2886,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2597,1342]) ).
thf(2887,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2886]) ).
thf(2888,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[2887:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(5435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3976,1019]) ).
thf(5436,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[5435]) ).
thf(5441,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) )
!= C )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[5436]) ).
thf(5446,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[5441]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(445,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[444]) ).
thf(446,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[445]) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ~ $true
| ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[629,446]) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[1583]) ).
thf(1585,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(pattern_uni,[status(thm)],[1584:[bind(A,$thf( tc_nat ))]]) ).
thf(1598,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[1585]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(2976,plain,
! [A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(paramod_ordered,[status(thm)],[990,2972]) ).
thf(2977,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(pattern_uni,[status(thm)],[2976:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero ))]]) ).
thf(1399,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
inference(polarity_switch,[status(thm)],[1398]) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
inference(lifteq,[status(thm)],[1399]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(2667,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2402,1342]) ).
thf(2668,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2667]) ).
thf(2669,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(pattern_uni,[status(thm)],[2668:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( K @ ( L @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(2678,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(simp,[status(thm)],[2669]) ).
thf(376,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1300,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(717,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(174,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(839,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(840,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(lifteq,[status(thm)],[839]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(951,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(1220,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(383,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1316,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1317,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(lifteq,[status(thm)],[1316]) ).
thf(59,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(581,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(582,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[581]) ).
thf(1830,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(rewrite,[status(thm)],[582,990]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(643,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1472,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ~ $true
| ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[629,439]) ).
thf(1473,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 )
!= ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
| ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B ) ),
inference(simp,[status(thm)],[1472]) ).
thf(1474,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
inference(pattern_uni,[status(thm)],[1473:[bind(A,$thf( tc_nat ))]]) ).
thf(1485,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= A ),
inference(simp,[status(thm)],[1474]) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
inference(polarity_switch,[status(thm)],[1425]) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
inference(lifteq,[status(thm)],[1426]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(859,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(9175,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9079,1292]) ).
thf(9176,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9175]) ).
thf(9215,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc @ c_Suc )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(simp,[status(thm)],[9176]) ).
thf(9235,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[9215]) ).
thf(10844,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( A @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
inference(paramod_ordered,[status(thm)],[990,9235]) ).
thf(10845,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(pattern_uni,[status(thm)],[10844:[bind(A,$thf( tc_nat @ c_HOL_Ozero__class_Ozero )),bind(B,$thf( B ))]]) ).
thf(10885,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[10845]) ).
thf(4440,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2042,4339]) ).
thf(4441,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4440]) ).
thf(4488,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4441]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(1353,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(1140,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(3115,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ~ $true
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2888,1342]) ).
thf(3116,plain,
! [A: $i] :
( ( ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( A @ c_InductTermi_OIT ) )
| ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[3115]) ).
thf(3117,plain,
v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT,
inference(pattern_uni,[status(thm)],[3116:[bind(A,$thf( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(248,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1008,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(571,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1272,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(611,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(polarity_switch,[status(thm)],[610]) ).
thf(612,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(lifteq,[status(thm)],[611]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(2086,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2079,431]) ).
thf(2087,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2086]) ).
thf(2088,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2087]) ).
thf(2043,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1848,431]) ).
thf(2044,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2043]) ).
thf(2045,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2044]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(1157,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(1412,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(330,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(1189,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(1289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(296,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(1108,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(976,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(688,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(366,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1276,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(388,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(1326,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(1101,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(4268,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3677,984]) ).
thf(4269,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[4268]) ).
thf(4311,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[4269]) ).
thf(4338,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[4311]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[515]) ).
thf(517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[516]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(5512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4410,1019]) ).
thf(5513,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5512]) ).
thf(5516,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C ) ),
inference(simp,[status(thm)],[5513]) ).
thf(5532,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[5516]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(cnf,[status(esa)],[432]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(213,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(929,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(380,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(1309,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(9843,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9109,984]) ).
thf(9844,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[9843]) ).
thf(9875,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc @ c_Suc )
!= C )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(simp,[status(thm)],[9844]) ).
thf(9887,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ c_Suc )
!= B ),
inference(simp,[status(thm)],[9875]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(118,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(716,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ c_Lambda_Obeta ) )
| ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Obeta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(1348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ c_Lambda_Obeta ) )
| ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Obeta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(134,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(752,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(3859,plain,
! [A: $i] :
( ( A
!= ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[963,2045]) ).
thf(3860,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( tc_nat @ ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[3859:[bind(A,$thf( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) ))]]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(9299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[3975,1019]) ).
thf(9300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) ) )
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[9299]) ).
thf(9301,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( B @ c_Lambda_OdB_OVar )
!= C )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= C )
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[9300]) ).
thf(9318,plain,
! [B: $i,A: $i] :
( ( ( B @ c_Lambda_OdB_OVar )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[9301]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ c_Lambda_Osubst ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ c_Lambda_Osubst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(999,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(75,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(620,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(1395,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(854,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(10278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[10262,1342]) ).
thf(10279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[10278]) ).
thf(10280,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
| ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(pattern_uni,[status(thm)],[10279:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( tc_nat @ c_HOL_Ozero__class_Ozero ))]]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(918,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
inference(cnf,[status(esa)],[505]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Olift ) )
= ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OApp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Olift ) )
= ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OApp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(796,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(193,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(886,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(334,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(1197,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[530]) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[531]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Lambda_Olift ) @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Lambda_Olift ) @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(2061,plain,
( ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2054,431]) ).
thf(2062,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[2061]) ).
thf(2063,plain,
( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) ),
inference(simp,[status(thm)],[2062]) ).
thf(4898,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ra @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[4188,984]) ).
thf(4899,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( v_ra @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4898]) ).
thf(4917,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != v_ra )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4899]) ).
thf(4923,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_ra @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4917]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1152,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(19117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[914,3178]) ).
thf(19118,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
!= ( tc_nat @ ( C @ ( C @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[19117]) ).
thf(19162,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= C )
| ( A
!= ( C @ c_Suc ) ) ),
inference(simp,[status(thm)],[19118]) ).
thf(19183,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= B ),
inference(simp,[status(thm)],[19162]) ).
thf(4456,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2048,4339]) ).
thf(4457,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_InductTermi_OIT )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4456]) ).
thf(4484,plain,
( ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ) )
| ( ( v_ja @ ( v_ia @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_OdB_OAbs @ c_Lambda_Osubst ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[4457]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(850,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(375,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(1299,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(3063,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ~ $true
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(paramod_ordered,[status(thm)],[2678,1342]) ).
thf(3064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT )
!= ( C @ c_InductTermi_OIT ) )
| ( C @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[3063]) ).
thf(3065,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(pattern_uni,[status(thm)],[3064:[bind(A,$thf( L )),bind(B,$thf( M )),bind(C,$thf( L @ ( M @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs ))]]) ).
thf(3076,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Lambda_OdB_OVar @ ( v_ra @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ),
inference(simp,[status(thm)],[3065]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
!= ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(500,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[499]) ).
thf(501,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[500]) ).
thf(77,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(624,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1236,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(987,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
inference(polarity_switch,[status(thm)],[1350]) ).
thf(1352,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
inference(lifteq,[status(thm)],[1351]) ).
thf(1383,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(cnf,[status(esa)],[1382]) ).
thf(1384,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(lifteq,[status(thm)],[1383]) ).
thf(1385,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Lambda_OdB_OVar @ A )
= B ),
inference(detectInverse,[status(thm)],[1384]) ).
thf(1386,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar @ sk5 )
= A ),
inference(cnf,[status(esa)],[1385]) ).
thf(1827,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar @ sk5 )
= A ),
inference(lifteq,[status(thm)],[1386]) ).
thf(358,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(1261,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(1268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(11593,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(simp,[status(thm)],[11570]) ).
thf(11601,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(simp,[status(thm)],[11593]) ).
thf(11764,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(rewrite,[status(thm)],[11601,990]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
| ( B @ ( A @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ ( A @ c_Lambda_Obeta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).
thf(1431,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
| ( B @ ( A @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ ( A @ c_Lambda_Obeta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(157,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(803,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(923,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(659,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(543,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(cnf,[status(esa)],[542]) ).
thf(1416,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Obeta ) ),
inference(polarity_switch,[status(thm)],[1415]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(755,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(10710,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(paramod_ordered,[status(thm)],[463,10683]) ).
thf(10711,plain,
( ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ~ ( tc_nat @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(pattern_uni,[status(thm)],[10710:[bind(A,$thf( tc_nat )),bind(B,$thf( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc )),bind(C,$thf( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc ))]]) ).
thf(10744,plain,
( ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) )
| ~ $true ),
inference(rewrite,[status(thm)],[10711,629,1077]) ).
thf(10745,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
!= ( tc_nat @ c_HOL_Oone__class_Oone ) ),
inference(simp,[status(thm)],[10744]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[467]) ).
thf(469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[468]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ c_Lambda_OdB_OApp ) @ ( A @ c_Lambda_Oliftn ) ) )
= ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OApp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ c_Lambda_OdB_OApp ) @ ( A @ c_Lambda_Oliftn ) ) )
= ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OApp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(216,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(935,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(261,axiom,
tc_nat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1037,plain,
tc_nat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(560,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[559]) ).
thf(453,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[452]) ).
thf(454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
inference(lifteq,[status(thm)],[453]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(1069,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(30714,plain,
$false,
inference(e,[status(thm)],[892,1322,4188,809,629,4169,479,3666,846,1840,518,1110,481,5088,1369,1190,2336,1454,909,3979,523,1406,20798,4339,5644,994,1401,2947,1728,449,440,677,1305,1173,10262,741,1073,2114,1142,1078,1137,9127,550,4220,472,1233,814,698,1342,11055,2042,538,19180,9233,533,945,7452,829,898,2972,1391,709,841,973,1359,2082,1366,436,1265,651,1228,1254,3976,20340,504,1323,1191,1132,724,1055,1409,1313,1279,542,460,559,1379,1087,1147,1609,1115,1362,1100,817,902,606,5323,1398,881,1415,5663,2105,591,443,1040,2122,1828,514,1020,806,966,1183,1334,646,485,834,1051,821,766,1843,687,1377,3189,634,877,6772,1242,507,527,4483,1119,774,428,1201,452,920,5751,1438,761,1067,714,4172,512,942,439,546,793,1338,5142,798,1057,1163,1274,1387,746,1343,778,1042,862,561,630,429,788,729,957,1223,1217,598,1423,467,625,879,1178,461,9132,493,1027,757,1281,842,1012,1106,566,484,852,2663,7503,1296,665,583,830,551,1128,1392,11602,1291,11420,710,1350,1089,2115,948,4512,1064,1425,1006,610,499,989,1270,1851,980,1498,1082,488,669,526,637,489,1214,2108,884,1329,1160,2877,1292,933,554,753,901,476,1016,1207,2085,679,970,1155,547,1324,985,738,1382,3059,1192,10961,1002,1627,647,1263,515,1150,1060,1050,984,911,1318,20451,938,805,508,921,541,1167,530,586,662,926,2057,1054,2076,1170,1286,1035,558,1071,2402,1187,674,953,1185,906,10683,618,430,2391,1103,856,444,1374,19178,733,819,904,2048,1389,772,579,2991,1256,843,1125,826,577,1428,936,1371,1312,498,1239,1332,7924,7455,1258,1356,672,466,1092,1194,2079,9560,1209,900,681,1048,3106,451,737,1376,6942,7933,784,1117,990,996,2955,1492,509,649,1043,434,616,1122,4477,1307,890,811,9129,1080,1339,552,535,9079,594,726,621,3977,895,964,915,769,1022,1293,6660,848,700,520,1198,959,868,455,1435,6100,3178,431,653,922,4481,2069,521,3480,1171,983,2075,2051,695,1245,1176,608,1113,563,1726,1364,1250,10186,505,490,1304,1166,589,2878,812,553,5812,473,1076,2054,722,663,548,9884,1420,927,20509,1134,487,1081,749,3975,1145,1018,2597,19182,968,458,1181,823,4812,836,776,640,1025,887,1252,7462,1267,1230,2888,5446,1845,712,557,690,1598,705,2977,2060,1400,707,739,2678,1053,1300,791,441,1038,717,502,840,463,951,1130,1220,544,1317,1830,1085,470,1336,643,9109,744,703,2992,613,1485,1427,876,859,991,656,10885,4488,1284,1353,600,1094,978,1140,3117,1008,446,571,1272,612,627,2088,2045,556,482,5536,1157,1412,759,1189,4170,1289,1108,1316,450,1084,931,539,976,688,3188,524,581,1276,1326,961,1341,1062,1101,632,4338,781,963,517,731,786,1030,3978,914,5532,433,667,929,9223,2066,1212,763,1309,9887,549,536,1045,1077,3677,832,684,716,800,1348,752,447,3860,432,1097,9318,1380,1248,865,603,999,620,1395,1625,854,1303,10280,5760,735,3164,918,506,437,767,828,720,955,796,886,1033,2961,1197,9883,532,1346,2063,4923,9235,1152,19183,1019,7457,4484,4410,850,1299,3076,871,501,624,839,1236,987,1352,464,1827,1261,1268,575,596,11764,1431,1004,803,1320,923,659,543,1848,1416,755,10745,1204,469,940,935,1009,1037,560,496,454,1069,1014,1417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 23:29:46 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.44/1.43 % [INFO] Parsing done (432ms).
% 2.44/1.45 % [INFO] Running in sequential loop mode.
% 3.52/1.83 % [INFO] eprover registered as external prover.
% 3.52/1.84 % [INFO] Scanning for conjecture ...
% 3.71/2.03 % [INFO] Found a conjecture (or negated_conjecture) and 715 axioms. Running axiom selection ...
% 4.91/2.26 % [INFO] Axiom selection finished. Selected 424 axioms (removed 291 axioms).
% 5.81/2.48 % [INFO] Problem is propositional (TPTP CNF).
% 5.81/2.50 % [INFO] Type checking passed.
% 6.13/2.50 % [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 ...
% 100.31/22.17 % External prover 'e' found a proof!
% 100.31/22.17 % [INFO] Killing All external provers ...
% 100.31/22.17 % Time passed: 21601ms (effective reasoning time: 20711ms)
% 100.31/22.17 % 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
% 100.31/22.17 % No. of inferences in proof: 1445
% 100.31/22.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 21601 ms resp. 20711 ms w/o parsing
% 100.04/22.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 100.04/22.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------