%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA021-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 06:50:17 AM UTC 2026
% Result : Unsatisfiable 41.14s 10.24s
% Output : Refutation 41.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1064
% Syntax : Number of formulae : 2160 ( 472 unt; 0 typ; 0 def)
% Number of atoms : 5674 (1147 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 25739 (3284 ~;3506 |; 0 &;18949 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 94 usr; 15 con; 0-3 aty)
% Number of variables : 4085 ( 0 ^;4085 !; 0 ?;4085 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_f_decl,type,
v_f: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(v_c_decl,type,
v_c: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_h_decl,type,
v_h: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Divides_Oop_Amod_decl,type,
c_Divides_Oop_Amod: $i > $i > $i > $i ).
thf(c_Numeral_Onumber__of_decl,type,
c_Numeral_Onumber__of: $i > $i > $i ).
thf(c_Numeral_OBit_decl,type,
c_Numeral_OBit: $i > $i > $i ).
thf(c_Numeral_OPls_decl,type,
c_Numeral_OPls: $i ).
thf(c_Numeral_Obit_OB1_decl,type,
c_Numeral_Obit_OB1: $i ).
thf(c_Numeral_Obit_OB0_decl,type,
c_Numeral_Obit_OB0: $i ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(c_1_decl,type,
c_1: $i ).
thf(class_Numeral_Onumber__ring_decl,type,
class_Numeral_Onumber__ring: $i > $o ).
thf(c_IntDef_Oiszero_decl,type,
c_IntDef_Oiszero: $i > $i > $o ).
thf(c_Numeral_Obin__add_decl,type,
c_Numeral_Obin__add: $i > $i > $i ).
thf(c_Numeral_Obin__minus_decl,type,
c_Numeral_Obin__minus: $i > $i ).
thf(c_IntDef_Oneg_decl,type,
c_IntDef_Oneg: $i > $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_div_decl,type,
c_div: $i > $i > $i > $i ).
thf(c_Numeral_Obin__succ_decl,type,
c_Numeral_Obin__succ: $i > $i ).
thf(class_Ring__and__Field_Odivision__by__zero_decl,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(c_divide_decl,type,
c_divide: $i > $i > $i > $i ).
thf(class_Power_Orecpower_decl,type,
class_Power_Orecpower: $i > $o ).
thf(c_Nat_Opower_decl,type,
c_Nat_Opower: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_Numeral_OMin_decl,type,
c_Numeral_OMin: $i ).
thf(class_Numeral_Onumber_decl,type,
class_Numeral_Onumber: $i > $o ).
thf(c_Numeral_Obin__mult_decl,type,
c_Numeral_Obin__mult: $i > $i > $i ).
thf(c_Parity_Oeven_decl,type,
c_Parity_Oeven: $i > $i > $o ).
thf(c_Divides_Oop_Advd_decl,type,
c_Divides_Oop_Advd: $i > $i > $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(c_IntDef_Oint_decl,type,
c_IntDef_Oint: $i > $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group_decl,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
thf(c_LOrder_Omeet_decl,type,
c_LOrder_Omeet: $i > $i > $i > $i ).
thf(c_LOrder_Ojoin_decl,type,
c_LOrder_Ojoin: $i > $i > $i > $i ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_decl,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_HOL_Oinverse_decl,type,
c_HOL_Oinverse: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_IntDef_Onat_decl,type,
c_IntDef_Onat: $i > $i ).
thf(c_NatArith_Oof__nat_decl,type,
c_NatArith_Oof__nat: $i > $i > $i ).
thf(class_LOrder_Omeet__semilorder_decl,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(c_List_Odrop_decl,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0__cancel_decl,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__meet_decl,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__join_decl,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_LOrder_Olorder_decl,type,
class_LOrder_Olorder: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_decl,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
thf(c_IntDef_Oof__int_decl,type,
c_IntDef_Oof__int: $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__abs__if_decl,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
thf(c_Binomial_Obinomial_decl,type,
c_Binomial_Obinomial: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_List_Ochar_OChar_decl,type,
c_List_Ochar_OChar: $i > $i > $i ).
thf(c_OrderedGroup_Onprt_decl,type,
c_OrderedGroup_Onprt: $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_decl,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_OrderedGroup_Opprt_decl,type,
c_OrderedGroup_Opprt: $i > $i > $i ).
thf(c_SetInterval_OgreaterThanAtMost_decl,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Main_Omod__eq__0D__dest__1_decl,type,
c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).
thf(c_Main_Ozmod__eq__0D__dest__1_decl,type,
c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).
thf(c_List_Olexn_decl,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(tc_List_Ochar_decl,type,
tc_List_Ochar: $i ).
thf(694,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
thf(2630,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
thf(1718,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(450,axiom,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_IntDef_Oneg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
thf(2094,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_IntDef_Oneg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
thf(1823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(830,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
thf(2921,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1064,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(3449,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
thf(1818,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(540,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(2280,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__neg_0) ).
thf(1686,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(880,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( c_0
!= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_0) ).
thf(3021,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( c_0
!= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(686,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(2612,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
thf(1469,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_plus ) ) )
= ( A @ ( B @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_plus ) ) )
= ( A @ ( B @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(547,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(2295,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_plus ) ) @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
thf(2341,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_plus ) ) @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(565,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
thf(2336,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(874,axiom,
! [A: $i] :
( ( c_1 != c_0 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__neq__zero_0) ).
thf(3008,plain,
! [A: $i] :
( ( c_1 != c_0 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(166,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
thf(1454,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_minus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
thf(2031,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_minus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(1057,axiom,
( c_1
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(3434,plain,
( c_1
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(944,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
thf(3167,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(597,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_51) ).
thf(2412,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(808,axiom,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(2876,plain,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(621,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
thf(2463,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1042,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = c_0 )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
thf(3397,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = c_0 )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_1) ).
thf(1899,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(1850,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(636,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(2499,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(604,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(2427,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
thf(1081,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1082,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(cnf,[status(esa)],[1081]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[1082]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
thf(2077,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(299,axiom,
( ( tc_nat @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).
thf(1750,plain,
( ( tc_nat @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1010,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
thf(3317,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(2,negated_conjecture,
t_a @ ( v_c @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(1068,plain,
t_a @ ( v_c @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(707,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(2659,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(649,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
thf(2527,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(4,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(1070,plain,
v_x != c_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1072,plain,
v_x != c_0,
inference(polarity_switch,[status(thm)],[1070]) ).
thf(1073,plain,
v_x != c_0,
inference(lifteq,[status(thm)],[1072]) ).
thf(273,axiom,
~ ( tc_IntDef_Oint @ ( c_1 @ c_Parity_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
thf(1692,plain,
~ ( tc_IntDef_Oint @ ( c_1 @ c_Parity_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1036,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(3382,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
thf(1173,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(553,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(2309,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(857,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(2976,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(777,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
thf(2808,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__less__divide__1__iff_1) ).
thf(1522,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(634,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(2495,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(585,axiom,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( A @ ( B @ c_div ) ) @ c_plus ) ) ) )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
thf(2381,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( A @ ( B @ c_div ) ) @ c_plus ) ) ) )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(591,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
thf(2395,plain,
c_0 != c_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(824,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_1) ).
thf(2908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(846,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
thf(2953,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__pos_0) ).
thf(1401,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
thf(1422,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(218,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(1569,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(714,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_8) ).
thf(2671,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
thf(1544,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(2676,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_divide ) ) )
= ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus1__divide_0) ).
thf(2014,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_divide ) ) )
= ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(453,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(2099,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
thf(2282,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_3) ).
thf(1591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(460,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_15) ).
thf(2114,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
thf(1142,plain,
! [B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(85,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2_0) ).
thf(1269,plain,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(1793,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(798,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
thf(2854,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__mult ) )
= c_Numeral_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
thf(1608,plain,
! [A: $i] :
( ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__mult ) )
= c_Numeral_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(32,axiom,
! [A: $i] :
( ( c_Numeral_OPls @ ( A @ c_Numeral_Obin__add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
thf(1137,plain,
! [A: $i] :
( ( c_Numeral_OPls @ ( A @ c_Numeral_Obin__add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(721,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_6) ).
thf(2686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ c_Suc @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_1 @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
thf(1756,plain,
! [A: $i] :
( ( A @ c_Suc @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_1 @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(928,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
thf(3135,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(948,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
thf(3175,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1018,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
thf(3338,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(71,axiom,
( ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
thf(1233,plain,
( ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(693,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_1) ).
thf(2627,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1048,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
thf(3414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(426,axiom,
! [A: $i] :
( ( ( A @ c_IntDef_Onat @ c_IntDef_Oint )
= c_0 )
| ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
thf(2042,plain,
! [A: $i] :
( ( ( A @ c_IntDef_Onat @ c_IntDef_Oint )
= c_0 )
| ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_1 )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_1 )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( c_0 @ ( C @ c_times ) ) @ ( A @ ( c_0 @ ( B @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if_0) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( c_0 @ ( C @ c_times ) ) @ ( A @ ( c_0 @ ( B @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
thf(1426,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(872,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
thf(3004,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
thf(2035,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1029,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(3365,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(745,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
thf(2740,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__pos_1) ).
thf(1999,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
thf(2316,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(1275,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(474,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(2141,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(607,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
thf(2434,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ( c_1
= ( A @ ( B @ ( B @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oeq__divide__eq__1_2) ).
thf(1872,plain,
! [B: $i,A: $i] :
( ( c_1
= ( A @ ( B @ ( B @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(372,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
thf(1919,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(619,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( B @ c_Nat_Opower ) ) @ ( A @ ( C @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
thf(2459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( B @ c_Nat_Opower ) ) @ ( A @ ( C @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(821,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Omeet ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
thf(2901,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Omeet ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1008,axiom,
( ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) )
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
thf(3313,plain,
( ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) )
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(388,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
thf(1954,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(793,axiom,
! [A: $i] :
( ( c_0
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_2) ).
thf(2844,plain,
! [A: $i] :
( ( c_0
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= ( A @ ( C @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= ( A @ ( C @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(576,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_Nat_Opower ) ) @ ( A @ ( B @ ( D @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( A @ ( D @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
thf(2360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_Nat_Opower ) ) @ ( A @ ( B @ ( D @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( A @ ( D @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(991,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= B )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
thf(3276,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= B )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(668,axiom,
tc_nat @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(2575,plain,
tc_nat @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1031,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
thf(3370,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(914,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
thf(3103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(737,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(2723,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(855,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_11) ).
thf(2972,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
thf(1914,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(657,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
thf(2548,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(980,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= ( A @ ( C @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
thf(3249,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= ( A @ ( C @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ c_HOL_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__inverse__eq_0) ).
thf(2020,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ c_HOL_Oinverse ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(123,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oinverse ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1) ).
thf(1359,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oinverse ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(444,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
thf(2082,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(782,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
thf(2819,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(242,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_60) ).
thf(1623,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_times ) ) @ ( B @ c_divide ) ) )
= ( A @ ( C @ ( c_1 @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if1_1) ).
thf(1887,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_times ) ) @ ( B @ c_divide ) ) )
= ( A @ ( C @ ( c_1 @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(848,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
thf(2957,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(1017,axiom,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
thf(3335,plain,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(56,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
thf(1196,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(862,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(2985,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(221,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1576,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1006,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(3308,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(380,axiom,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Onat @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_2) ).
thf(1935,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Onat @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) )
= c_0 )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_1) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) )
= c_0 )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) )
= ( A @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) )
= ( A @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_0) ).
thf(1921,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
thf(1386,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(993,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
thf(3281,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= ( tc_nat @ ( C @ ( B @ c_div ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(930,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(3140,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
thf(1475,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(705,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(2654,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
thf(1709,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(828,axiom,
! [A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_IntDef_Oof__int ) )
= ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
thf(2916,plain,
! [A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_IntDef_Oof__int ) )
= ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(957,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
thf(3195,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__neg_0) ).
thf(1430,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(425,axiom,
! [A: $i] :
( ( A
= ( c_0 @ c_Suc ) )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
thf(2039,plain,
! [A: $i] :
( ( A
= ( c_0 @ c_Suc ) )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(304,axiom,
( ( tc_IntDef_Oint @ ( c_0 @ c_IntDef_Oint @ c_uminus ) )
= ( c_0 @ c_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
thf(1760,plain,
( ( tc_IntDef_Oint @ ( c_0 @ c_IntDef_Oint @ c_uminus ) )
= ( c_0 @ c_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(712,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_31) ).
thf(2667,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(534,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(2269,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
thf(2755,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(897,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
thf(3061,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(731,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
thf(2708,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( C @ c_plus ) ) )
= ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
thf(1313,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1024,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(3353,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
thf(2126,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(729,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(2703,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_0) ).
thf(1287,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(968,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
thf(3221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(367,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(1907,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(637,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
thf(2501,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= ( A @ ( C @ ( D @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__right_0) ).
thf(1330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= ( A @ ( C @ ( D @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__mult ) )
= ( c_Numeral_Obit_OB0 @ ( B @ ( A @ c_Numeral_Obin__mult ) @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ( B @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__mult ) )
= ( c_Numeral_Obit_OB0 @ ( B @ ( A @ c_Numeral_Obin__mult ) @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
thf(2217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(108,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
thf(1323,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(935,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(3148,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(495,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_50) ).
thf(2185,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_5) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(818,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(2897,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(54,axiom,
( ( c_Numeral_OMin @ c_Numeral_Obin__minus )
= ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
thf(1191,plain,
( ( c_Numeral_OMin @ c_Numeral_Obin__minus )
= ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Ojoin ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Omeet ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
thf(1462,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Ojoin ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Omeet ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(889,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(3043,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(666,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
thf(2571,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(574,axiom,
! [A: $i] :
( ( c_0 @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
thf(2356,plain,
! [A: $i] :
( ( c_0 @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(601,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_0) ).
thf(2420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(912,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= ( tc_nat @ ( c_0 @ ( B @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(3099,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= ( tc_nat @ ( c_0 @ ( B @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(733,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(2713,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( C @ ( B @ c_Numeral_Obin__mult ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
thf(2169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( C @ ( B @ c_Numeral_Obin__mult ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__divide_0) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(377,axiom,
( ( c_1 @ c_IntDef_Onat )
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
thf(1931,plain,
( ( c_1 @ c_IntDef_Onat )
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
thf(1773,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( A @ ( c_0 @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
thf(1362,plain,
! [A: $i] :
( ~ ( A @ ( c_0 @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(651,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_52) ).
thf(2533,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(786,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(2829,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(360,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
thf(1892,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1033,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(3374,plain,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(278,axiom,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
thf(1704,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
thf(1890,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(876,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__negative__iff__negative_0) ).
thf(3014,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(646,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(2520,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
thf(2852,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(973,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
thf(3231,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1012,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(3322,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(959,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
thf(3199,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
thf(2090,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_7) ).
thf(1632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_div ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
thf(2259,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_div ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(942,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
thf(3163,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)],[942]) ).
thf(38,axiom,
! [A: $i] :
( ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__minus )
= ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_Obin__minus @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
thf(1151,plain,
! [A: $i] :
( ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__minus )
= ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_Obin__minus @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(564,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(2335,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__minus1_0) ).
thf(2017,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(688,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
thf(2616,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( c_1
!= ( A @ ( C @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oeq__divide__eq__1_1) ).
thf(1946,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( c_1
!= ( A @ ( C @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_4) ).
thf(1465,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( C @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
thf(2324,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( C @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_4) ).
thf(1714,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(129,axiom,
! [A: $i] :
( ( ( A @ c_IntDef_Onat )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
thf(1373,plain,
! [A: $i] :
( ( ( A @ c_IntDef_Onat )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(868,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(2996,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_4) ).
thf(1911,plain,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(764,axiom,
tc_nat @ class_LOrder_Olorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(2782,plain,
tc_nat @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(615,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(2451,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1059,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
thf(3438,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(465,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).
thf(2122,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(832,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(2925,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(399,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(1978,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(133,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(1383,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
thf(2254,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
thf(1960,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(997,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
thf(3290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1002,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
thf(3300,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(910,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
thf(3093,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(762,axiom,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( A @ ( B @ c_div ) ) @ c_plus ) ) ) )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
thf(2777,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( A @ ( B @ c_div ) ) @ c_plus ) ) ) )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(937,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(3152,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(51,axiom,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_1 )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_0) ).
thf(1183,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_1 )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(439,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_plus ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(801,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
thf(2861,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(630,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
thf(2483,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
thf(1351,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(698,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(2639,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(852,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
thf(2965,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( B
= ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_3) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( B
= ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ c_Numeral_OBit ) @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) )
= ( C @ ( B @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ c_Numeral_OBit ) @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) )
= ( C @ ( B @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(735,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(2718,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1039,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
thf(3389,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(640,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(2508,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_divide ) ) )
= C )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_3) ).
thf(2058,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_divide ) ) )
= C )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(579,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_HOL_Oabs ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
thf(2367,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_HOL_Oabs ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(608,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0) ).
thf(2437,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_times ) ) @ c_divide ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if2_1) ).
thf(1928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_times ) ) @ c_divide ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(689,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
thf(2618,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(788,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
thf(2833,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_minus ) ) @ c_minus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(954,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(3189,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_divide ) ) @ ( B @ c_times ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__eq__1_0) ).
thf(1896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_divide ) ) @ ( B @ c_times ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(1051,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
thf(3421,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(886,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
thf(3036,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(650,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_times ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
thf(2530,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_times ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
thf(1119,plain,
! [A: $i] :
( ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(241,axiom,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_1) ).
thf(1622,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(859,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).
thf(2979,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_9) ).
thf(1526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(472,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
thf(2137,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_divide ) ) @ c_times ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__eq__2_0) ).
thf(2103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_divide ) ) @ c_times ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(749,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).
thf(2750,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(144,axiom,
( ( c_Numeral_OMin @ c_Numeral_Obin__succ )
= c_Numeral_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
thf(1405,plain,
( ( c_Numeral_OMin @ c_Numeral_Obin__succ )
= c_Numeral_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(589,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
thf(2392,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(480,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(2154,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_divide ) ) )
= ( A @ ( C @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__divide__divide_0) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_divide ) ) )
= ( A @ ( C @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(673,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
thf(2586,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_5) ).
thf(1975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Onat ) )
| ( ( A @ c_IntDef_Oint )
!= ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
thf(1564,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Onat ) )
| ( ( A @ c_IntDef_Oint )
!= ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(754,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0) ).
thf(2762,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(1034,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(3376,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(3377,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(polarity_switch,[status(thm)],[3376]) ).
thf(3378,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(lifteq,[status(thm)],[3377]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(1863,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(5,negated_conjecture,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(1065,plain,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1074,plain,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[1065]) ).
thf(972,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
thf(3229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(825,axiom,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(2910,plain,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(626,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
thf(2473,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(462,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(2118,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__eq__iff__eq_0) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Oinverse ) )
!= ( A @ ( C @ c_HOL_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(428,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
thf(2047,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1050,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = D )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= ( A @ ( D @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).
thf(3418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = D )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= ( A @ ( D @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(875,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( ( A @ c_IntDef_Oint )
!= ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
thf(3011,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( ( A @ c_IntDef_Oint )
!= ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1003,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).
thf(3301,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(504,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).
thf(2204,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(945,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(3169,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(986,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(3265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(702,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_IntDef_Onat @ ( A @ c_IntDef_Onat @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
thf(2646,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_IntDef_Onat @ ( A @ c_IntDef_Onat @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(57,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__Suc__Suc_0) ).
thf(1199,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(578,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
thf(2364,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(485,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_42) ).
thf(2164,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( c_0
!= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( c_0
!= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(952,axiom,
( ( c_0 @ c_Suc )
= ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
thf(3186,plain,
( ( c_0 @ c_Suc )
= ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__neg_1) ).
thf(1311,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
thf(2232,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(552,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
thf(2307,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(894,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(3054,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(6,negated_conjecture,
t_a @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(1067,plain,
t_a @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(1736,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(691,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
thf(2621,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(708,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_5) ).
thf(2660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(308,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_1) ).
thf(1768,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_3) ).
thf(1868,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_8) ).
thf(2061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(760,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
thf(2773,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(249,axiom,
! [A: $i] :
( ( ( A @ c_IntDef_Onat @ c_IntDef_Oint )
= A )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
thf(1636,plain,
! [A: $i] :
( ( ( A @ c_IntDef_Onat @ c_IntDef_Oint )
= A )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
thf(1730,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(43,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_1) ).
thf(1163,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(610,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
thf(2441,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(674,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_8) ).
thf(2589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(730,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) @ c_HOL_Oabs ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
thf(2705,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) @ c_HOL_Oabs ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
thf(1723,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(680,axiom,
tc_nat @ class_Numeral_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
thf(2601,plain,
tc_nat @ class_Numeral_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Ojoin ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
thf(2249,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Ojoin ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(678,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
thf(2596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_minus ) ) )
= ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_minus ) ) )
= ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(266,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_NatArith_Oof__nat ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
thf(1676,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_NatArith_Oof__nat ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(477,axiom,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( c_0 @ c_Suc ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
thf(2147,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( c_0 @ c_Suc ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
thf(1502,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(854,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(2969,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(974,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(3233,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
thf(2606,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(863,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
thf(2986,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(963,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
thf(3207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(73,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
thf(1238,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(662,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
thf(2560,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(775,axiom,
! [A: $i] :
( ( A @ class_Numeral_Onumber )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
thf(2805,plain,
! [A: $i] :
( ( A @ class_Numeral_Onumber )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(538,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(2277,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_1) ).
thf(1355,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__0__1__iff_0) ).
thf(1580,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(938,axiom,
! [A: $i] :
( ( c_0 @ c_Suc @ ( A @ c_Binomial_Obinomial ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
thf(3154,plain,
! [A: $i] :
( ( c_0 @ c_Suc @ ( A @ c_Binomial_Obinomial ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(927,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(3134,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( c_0 @ c_times ) ) @ ( A @ ( B @ ( c_0 @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if_0) ).
thf(1619,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( c_0 @ c_times ) ) @ ( A @ ( B @ ( c_0 @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(478,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(2150,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_times ) ) )
= ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_times ) ) )
= ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(598,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(2414,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(470,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Nat_Opower ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( A @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
thf(2132,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Nat_Opower ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( A @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(815,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
thf(2890,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(995,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(3286,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(1883,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(988,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
thf(3269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__eq__1_1) ).
thf(1365,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_12) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_divide ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__eq__1_2) ).
thf(1951,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_divide ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( D @ c_times ) ) @ ( A @ ( B @ ( C @ c_times ) ) @ c_divide ) ) )
= ( A @ ( D @ ( C @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if_1) ).
thf(1457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( D @ c_times ) ) @ ( A @ ( B @ ( C @ c_times ) ) @ c_divide ) ) )
= ( A @ ( D @ ( C @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(502,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_div ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
thf(2200,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(492,axiom,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_Binomial_Obinomial ) @ ( B @ ( A @ c_Binomial_Obinomial ) @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
thf(2179,plain,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_Binomial_Obinomial ) @ ( B @ ( A @ c_Binomial_Obinomial ) @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_times ) ) )
= ( A @ ( C @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
thf(1656,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_times ) ) )
= ( A @ ( C @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(459,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(2112,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= ( A @ ( C @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
thf(1573,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= ( A @ ( C @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(19,axiom,
! [A: $i] :
( ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__succ )
= ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
thf(1106,plain,
! [A: $i] :
( ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__succ )
= ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(989,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ ( c_1 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
thf(3271,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ ( c_1 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(612,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
thf(2445,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(955,axiom,
! [A: $i] :
( ( A @ c_Suc @ ( c_0 @ c_Binomial_Obinomial ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
thf(3191,plain,
! [A: $i] :
( ( A @ c_Suc @ ( c_0 @ c_Binomial_Obinomial ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
thf(1938,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(752,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
thf(2758,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1044,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
thf(3403,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__0__1__iff_1) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(908,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
thf(3090,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__pos_0) ).
thf(1555,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(562,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(2332,plain,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(785,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
thf(2826,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(337,axiom,
! [A: $i] :
( ( ( A @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
thf(1836,plain,
! [A: $i] :
( ( ( A @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(493,axiom,
! [A: $i] :
( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
thf(2181,plain,
! [A: $i] :
( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(561,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
thf(2327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
thf(2213,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(883,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_2) ).
thf(3028,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(892,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(3050,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(569,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_13) ).
thf(2345,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(507,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
thf(2211,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_times ) ) )
= C )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_0) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_times ) ) )
= C )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(555,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
thf(2313,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) )
= c_1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
thf(1128,plain,
! [A: $i] :
( ( ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) )
= c_1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(248,axiom,
( ( c_0 @ c_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
thf(1634,plain,
( ( c_0 @ c_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(515,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
thf(2228,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(885,axiom,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
thf(3033,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1046,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( C @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(3408,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( C @ ( A @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ ( c_Numeral_OMin @ c_Numeral_Obin__mult ) )
= ( A @ c_Numeral_Obin__minus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
thf(1740,plain,
! [A: $i] :
( ( A @ ( c_Numeral_OMin @ c_Numeral_Obin__mult ) )
= ( A @ c_Numeral_Obin__minus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(915,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
thf(3105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( C @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_div ) ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_1) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( C @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_div ) ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(201,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(1534,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__divide__1__iff_0) ).
thf(1804,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(817,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
thf(2895,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
thf(1328,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_minus ) ) )
= ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_minus ) ) )
= ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(967,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( B @ ( c_0 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
thf(3218,plain,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( B @ ( c_0 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1038,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(3386,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(921,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= ( A @ ( C @ ( D @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).
thf(3119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= ( A @ ( C @ ( D @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_2) ).
thf(1762,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(644,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1) ).
thf(2515,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(922,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(3122,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(843,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
thf(2946,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(865,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
thf(2990,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(21,axiom,
! [A: $i] :
( ( ( A @ ( c_1 @ ( c_1 @ c_plus ) ) )
= ( A @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
thf(1111,plain,
! [A: $i] :
( ( ( A @ ( c_1 @ ( c_1 @ c_plus ) ) )
= ( A @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(1970,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(68,axiom,
! [A: $i] :
( ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__succ )
= ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_Obin__succ @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
thf(1227,plain,
! [A: $i] :
( ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__succ )
= ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_Obin__succ @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(724,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(2692,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(226,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(1587,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(641,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
thf(2509,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
thf(1672,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(800,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( B @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
thf(2858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( B @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(653,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
thf(2537,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1060,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
thf(3440,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(962,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(3205,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(907,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(3087,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(878,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(3018,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_3) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
thf(1567,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(184,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).
thf(1493,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(418,axiom,
! [A: $i] :
( ( A @ ( c_1 @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
thf(2023,plain,
! [A: $i] :
( ( A @ ( c_1 @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(932,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
thf(3143,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(870,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(3000,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_0) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(804,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( B @ c_Suc @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
thf(2868,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( B @ c_Suc @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(7,axiom,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_1 )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_1) ).
thf(1075,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_1 )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(658,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( c_0 @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
thf(2551,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( c_0 @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(711,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(2666,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_0
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oeq__divide__eq__number__of_2) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ( c_0
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(809,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
thf(2877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
thf(1942,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(258,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(1659,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(152,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(1424,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1061,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
thf(3441,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__pos_1) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
thf(2196,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(521,axiom,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_1 @ c_Divides_Oop_Amod ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
thf(2240,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Suc @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_1 @ c_Divides_Oop_Amod ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(488,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
thf(2172,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1054,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
thf(3428,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(1810,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_IntDef_Onat @ ( A @ c_IntDef_Onat @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
thf(1791,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_IntDef_Onat @ ( A @ c_IntDef_Onat @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(571,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_minus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
thf(2349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_minus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(2108,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
thf(1446,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(237,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ ( c_1 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__divide__eq__0__iff_1) ).
thf(1612,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ ( c_1 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(625,axiom,
tc_nat @ class_Power_Orecpower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(2472,plain,
tc_nat @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(999,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(3294,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(297,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( A @ ( B @ ( c_0 @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if2_0) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( A @ ( B @ ( c_0 @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
thf(1478,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
thf(1131,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(639,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
thf(2505,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(635,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
thf(2497,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
thf(1984,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(979,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
thf(3247,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1016,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(3333,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
thf(1114,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
thf(1324,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(543,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(2285,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(836,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
thf(2932,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_7) ).
thf(1297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(719,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
thf(2681,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(790,axiom,
! [A: $i] :
( ( c_0
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
thf(2836,plain,
! [A: $i] :
( ( c_0
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(632,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_NatArith_Oof__nat ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
thf(2487,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_NatArith_Oof__nat ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(679,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
thf(2598,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_0 )
| ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( c_1
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ( c_1
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(820,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(2900,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(587,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
thf(2387,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( D @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_2) ).
thf(1831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( D @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(70,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_div ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
thf(1231,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_div ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(796,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).
thf(2851,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
thf(2243,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(671,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
thf(2581,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(622,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
thf(2465,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(664,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(2566,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_9) ).
thf(1799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
thf(1852,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(780,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ( ( A @ ( C @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
thf(2813,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ( ( A @ ( C @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(756,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(2766,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
thf(2052,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
thf(1246,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(898,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(3064,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_HOL_Oinverse ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__mult__distrib_0) ).
thf(1720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_HOL_Oinverse ) )
= ( A @ ( A @ ( C @ c_HOL_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(917,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le__neg_1) ).
thf(3109,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_2) ).
thf(1979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(901,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
thf(3074,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(905,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(3083,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(960,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(3201,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__less__divide__1__iff_0) ).
thf(1393,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
thf(1627,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(580,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
thf(2370,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(966,axiom,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
thf(3215,plain,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(1333,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_divide ) ) )
= ( A @ ( C @ ( c_0 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__left_1) ).
thf(1991,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_divide ) ) )
= ( A @ ( C @ ( c_0 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
thf(2926,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(314,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(1779,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(215,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
thf(1563,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(748,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_Suc @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
thf(2748,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_Suc @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(851,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_div ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
thf(2963,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(1,negated_conjecture,
( ( c_0 @ v_f )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1066,plain,
( ( c_0 @ v_f )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(1071,plain,
( ( c_0 @ v_f )
= c_0 ),
inference(lifteq,[status(thm)],[1066]) ).
thf(709,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_14) ).
thf(2662,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_5) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( A @ ( C @ ( B @ c_minus ) ) @ c_times ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_minus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
thf(2634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( A @ ( C @ ( B @ c_minus ) ) @ c_times ) ) )
= ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_minus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(157,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
thf(1434,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(346,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_NatArith_Oof__nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
thf(1857,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_NatArith_Oof__nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( C @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(970,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
thf(3225,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(992,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
thf(3279,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)],[992]) ).
thf(951,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(3183,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(812,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(2883,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(947,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
thf(3173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_9) ).
thf(1712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1005,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(3306,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(769,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
thf(2793,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__0__1__iff_0) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_3) ).
thf(1515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(512,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).
thf(2221,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(701,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(2645,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_HOL_Oabs ) @ c_Nat_Opower ) ) )
= ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
thf(2189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_HOL_Oabs ) @ c_Nat_Opower ) ) )
= ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(566,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
thf(2338,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(1996,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(366,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(1906,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
thf(2001,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(822,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
thf(2904,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_Nat_Opower ) ) @ ( A @ ( C @ ( B @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
thf(2556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_Nat_Opower ) ) @ ( A @ ( C @ ( B @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
thf(1483,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__neg_1) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(985,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( c_0
!= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
thf(3262,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( c_0
!= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(681,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_37) ).
thf(2602,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(31,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ ( A @ c_plus ) ) @ c_div ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
thf(1135,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ ( A @ c_plus ) ) @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(740,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(253,axiom,
tc_IntDef_Oint @ ( c_0 @ c_Parity_Oeven ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
thf(1648,plain,
tc_IntDef_Oint @ ( c_0 @ c_Parity_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__0__iff_2) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(1510,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(78,axiom,
( ( c_Numeral_OPls @ c_Numeral_Obin__succ )
= ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).
thf(1251,plain,
( ( c_Numeral_OPls @ c_Numeral_Obin__succ )
= ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_0) ).
thf(1764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) ) )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
thf(1146,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) ) )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(301,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Onat )
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
thf(1754,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Onat )
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1026,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(3358,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(527,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(2253,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(537,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).
thf(2275,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(422,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
thf(2033,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(983,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
thf(3257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( c_1
!= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
thf(1219,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( c_1
!= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(903,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le__neg_0) ).
thf(3079,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(298,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
thf(1747,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(840,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
thf(2941,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_uminus ) @ c_times ) ) )
= ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
thf(2028,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_uminus ) @ c_times ) ) )
= ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( c_1
!= ( A @ ( c_0 @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oeq__divide__eq__1_0) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ( c_1
!= ( A @ ( c_0 @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ ( c_1 @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
thf(1595,plain,
! [A: $i] :
( ( A @ ( c_1 @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(742,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(2734,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(918,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( c_1 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
thf(3111,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( c_1 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(990,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
thf(3274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__1__iff_1) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(739,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_4) ).
thf(2727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(371,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(1916,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(839,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( c_0 @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
thf(2938,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( A @ ( c_0 @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(3,negated_conjecture,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(1069,plain,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(3458,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1069,1074]) ).
thf(3459,plain,
! [A: $i] :
( ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[3458]) ).
thf(3461,plain,
! [A: $i] :
( ( t_a != t_a )
| ( ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) ) )
| ( ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) ) ) ),
inference(simp,[status(thm)],[3459]) ).
thf(3462,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) ) )
| ( ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) ) ) ),
inference(simp,[status(thm)],[3461]) ).
thf(3465,plain,
! [A: $i] :
( ( t_a != t_a )
| ( ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) )
| ( v_c != v_c )
| ( t_a != t_a )
| ( ( A @ c_Suc @ v_f )
!= ( v_x @ v_f ) ) ),
inference(simp,[status(thm)],[3462]) ).
thf(3478,plain,
! [A: $i] :
( ( ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) )
| ( ( A @ c_Suc @ v_f )
!= ( v_x @ v_f ) ) ),
inference(simp,[status(thm)],[3465]) ).
thf(3498,plain,
! [A: $i] :
( ( t_a != t_a )
| ( ( A @ c_Suc @ v_h )
!= ( v_x @ v_h ) )
| ( ( A @ c_Suc )
!= v_x ) ),
inference(simp,[status(thm)],[3478]) ).
thf(3504,plain,
! [A: $i] :
( ( ( A @ c_Suc @ v_h )
!= ( v_x @ v_h ) )
| ( ( A @ c_Suc )
!= v_x ) ),
inference(simp,[status(thm)],[3498]) ).
thf(768,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__positive__iff__positive_1) ).
thf(2791,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(767,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(2789,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(860,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
thf(2981,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(300,axiom,
! [A: $i] :
( ( A @ c_IntDef_Oint @ c_IntDef_Onat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
thf(1752,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ c_IntDef_Onat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(904,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(3081,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ ( A @ c_div ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
thf(1388,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ c_Suc @ c_Suc @ ( A @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ ( A @ c_div ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
thf(1535,plain,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_minus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_minus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(734,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
thf(2716,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
thf(1520,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
thf(1124,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
thf(2134,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(849,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
thf(2959,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(238,axiom,
( ( c_1 @ c_IntDef_Oint )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
thf(1615,plain,
( ( c_1 @ c_IntDef_Oint )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_0) ).
thf(1784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(982,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(3255,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(648,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_uminus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
thf(2525,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_uminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(795,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_48) ).
thf(2849,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(715,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(2674,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(665,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_Numeral_Obin__mult ) @ c_Numeral_Onumber__of ) @ c_times ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
thf(2568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_Numeral_Obin__mult ) @ c_Numeral_Onumber__of ) @ c_times ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
thf(1795,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
thf(2398,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(726,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_11) ).
thf(2695,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(182,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ ( c_1 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__eq__1__divide__iff_1) ).
thf(1488,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ ( c_1 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__neg_0) ).
thf(1786,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1058,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
thf(3436,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( c_Numeral_Obit_OB1 @ ( B @ c_Numeral_OBit ) @ ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) )
= ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_Obin__succ @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ( c_Numeral_Obit_OB1 @ ( B @ c_Numeral_OBit ) @ ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) )
= ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_Obin__succ @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(486,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
thf(2166,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(618,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(2457,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(81,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
thf(1258,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1004,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
thf(3304,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(1025,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
thf(3355,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
thf(1428,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(969,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(3223,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(484,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
thf(2161,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(1707,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(546,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(2293,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(893,axiom,
! [A: $i] :
( ( ( A @ ( c_1 @ c_HOL_Oabs ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
thf(3051,plain,
! [A: $i] :
( ( ( A @ ( c_1 @ c_HOL_Oabs ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1015,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
thf(3330,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(744,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
thf(2738,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(838,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
thf(2935,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(871,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
thf(3002,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
thf(2425,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1049,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(3416,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(667,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
thf(2573,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
thf(2358,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( c_1 @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_minus ) ) @ c_List_Odrop ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
thf(2319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( c_1 @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_minus ) ) @ c_List_Odrop ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(913,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
thf(3101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(700,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_0) ).
thf(2642,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(361,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
thf(1894,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_uminus ) @ c_divide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__minus__left_0) ).
thf(1806,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_uminus ) @ c_divide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
thf(1524,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__neg_1) ).
thf(1542,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1037,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(3384,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
thf(1307,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_minus ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( C @ ( A @ ( D @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_plus ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_minus ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( C @ ( A @ ( D @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_plus ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(442,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(2079,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(554,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_plus ) ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
thf(2311,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_plus ) ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
thf(1209,plain,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(463,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(2119,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_2) ).
thf(1282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(628,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(2478,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
thf(2084,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(976,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( c_0 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
thf(3238,plain,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( c_0 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(692,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Ojoin ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
thf(2624,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Ojoin ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(697,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( A @ c_div ) ) )
= ( tc_IntDef_Oint @ ( A @ c_uminus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
thf(2637,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( A @ c_div ) ) )
= ( tc_IntDef_Oint @ ( A @ c_uminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(602,axiom,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= B )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
thf(2422,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= B )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(542,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(2284,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(378,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
thf(1933,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
thf(2257,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
thf(1589,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_HOL_Oinverse ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0) ).
thf(1603,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_HOL_Oinverse ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(549,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_NatArith_Oof__nat ) )
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
thf(2299,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_NatArith_Oof__nat ) )
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(847,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
thf(2955,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(523,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
thf(2246,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(713,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(2669,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(461,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_21) ).
thf(2116,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(791,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse ) @ c_times ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
thf(2839,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse ) @ c_times ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__eq__1__pos_0) ).
thf(1771,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(841,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
thf(2943,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(842,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(2945,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(958,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
thf(3197,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
thf(1801,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Power_Orecpower )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(799,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
thf(2856,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(773,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(2802,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(929,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(3138,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(2378,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(272,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).
thf(1690,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(899,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
thf(3066,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_6) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(805,axiom,
! [A: $i] :
( ( ( A @ ( c_1 @ c_uminus ) )
= ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
thf(2871,plain,
! [A: $i] :
( ( ( A @ ( c_1 @ c_uminus ) )
= ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(130,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
thf(1376,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(568,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
thf(2343,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( B @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
thf(1630,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_times ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( B @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
thf(1821,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_8) ).
thf(1909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(943,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(3165,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(873,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
thf(3006,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(1344,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(539,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
thf(2278,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(826,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_Nat_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Nat_Opower ) ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
thf(2911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_Nat_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Nat_Opower ) ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
thf(1688,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(3055,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[3054]) ).
thf(3453,plain,
( ( ( t_a @ ( v_c @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1068,3055]) ).
thf(3454,plain,
( ( t_a @ ( v_c @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[3453]) ).
thf(3455,plain,
( ( tc_nat != t_a )
| ( v_c != c_0 )
| ( c_0 != c_0 ) ),
inference(simp,[status(thm)],[3454]) ).
thf(3456,plain,
( ( tc_nat != t_a )
| ( v_c != c_0 ) ),
inference(simp,[status(thm)],[3455]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_divide ) ) @ ( B @ c_divide ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__divide__eq__right_0) ).
thf(1667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_divide ) ) @ ( B @ c_divide ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_times ) ) @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( A @ ( B @ c_HOL_Oinverse ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__eq__1__iff_0) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( A @ ( B @ c_HOL_Oinverse ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(174,axiom,
( ( c_Numeral_OPls @ c_Numeral_Obin__minus )
= c_Numeral_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
thf(1471,plain,
( ( c_Numeral_OPls @ c_Numeral_Obin__minus )
= c_Numeral_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = c_0 )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__0__iff_0) ).
thf(2025,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = c_0 )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_1 )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(cnf,[status(esa)],[1078]) ).
thf(1080,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
= c_1 ) ),
inference(lifteq,[status(thm)],[1079]) ).
thf(695,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Onprt ) @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
thf(2632,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Onprt ) @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(685,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
thf(2610,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(882,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(3027,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_1) ).
thf(1557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(763,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(2780,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(533,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
thf(2267,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(596,axiom,
! [A: $i] :
( ~ ( A @ ( c_1 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
thf(2410,plain,
! [A: $i] :
( ~ ( A @ ( c_1 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(831,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
thf(2923,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ ( A @ ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1001,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(3298,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(806,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(2874,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(2542,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
thf(1460,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(526,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(2252,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(710,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
thf(2664,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(834,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
thf(2928,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(620,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
thf(2461,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(856,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(2974,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(936,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(3150,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(792,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
thf(2842,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_Nat_Opower ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__mult ) )
= ( B @ ( c_Numeral_Obit_OB0 @ ( B @ ( A @ c_Numeral_Obin__mult ) @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
thf(1171,plain,
! [B: $i,A: $i] :
( ( B @ ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__mult ) )
= ( B @ ( c_Numeral_Obit_OB0 @ ( B @ ( A @ c_Numeral_Obin__mult ) @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(375,axiom,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
thf(1926,plain,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(789,axiom,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(2835,plain,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_2) ).
thf(2086,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(473,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).
thf(2139,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(940,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
thf(3159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(1007,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( B @ ( C @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(3310,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( B @ ( C @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( c_0
!= ( A @ ( B @ ( c_1 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__eq__1__divide__iff_0) ).
thf(1496,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( c_0
!= ( A @ ( B @ ( c_1 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(949,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
thf(3178,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_4) ).
thf(1973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
thf(2069,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(758,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(2770,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(440,axiom,
! [A: $i] :
( ~ ( A @ ( c_0 @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
thf(2075,plain,
! [A: $i] :
( ~ ( A @ ( c_0 @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(600,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
thf(2418,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(339,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(1841,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(609,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
thf(2439,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(738,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_1) ).
thf(2725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(593,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
thf(2401,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs ) @ c_HOL_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__inverse_0) ).
thf(1699,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( B @ c_HOL_Oabs ) @ c_HOL_Oinverse ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1052,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(3423,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_5) ).
thf(2481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( C @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__pos_1) ).
thf(1528,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( C @ ( B @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(977,axiom,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
thf(3241,plain,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(771,axiom,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
thf(2797,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(877,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
thf(3016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(2752,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
thf(1775,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
thf(2592,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(177,axiom,
tc_nat @ ( c_0 @ c_Parity_Oeven ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
thf(1477,plain,
tc_nat @ ( c_0 @ c_Parity_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1013,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
thf(3325,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_Numeral_Onumber__of ) ) )
| ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(931,axiom,
tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
thf(3142,plain,
tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(652,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_4) ).
thf(2535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(454,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(2101,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(125,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
thf(1364,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(853,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
thf(2967,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1022,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( A @ ( B @ ( A @ ( c_0 @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
thf(3348,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( A @ ( B @ ( A @ ( c_0 @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
thf(2156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
thf(1694,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(725,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(2693,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(411,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
thf(2005,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_2) ).
thf(2054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1062,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(3444,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(326,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
thf(1809,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= c_1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(535,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_div ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
thf(2271,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_div ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(941,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le_0) ).
thf(3161,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
thf(2037,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(934,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
thf(3146,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(614,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(2449,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_minus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
thf(2333,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_minus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
thf(1551,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(781,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
thf(2816,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(827,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
thf(2914,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(884,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
thf(3031,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(687,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
thf(2614,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_1) ).
thf(2096,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Ojoin ) ) )
= B )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
thf(1304,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Ojoin ) ) )
= B )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(956,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(3193,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
thf(1758,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
thf(1467,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(867,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(2994,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(638,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__negative__iff__negative_1) ).
thf(2503,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_divide ) ) )
= ( A @ ( c_0 @ ( C @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__right_1) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_divide ) ) )
= ( A @ ( c_0 @ ( C @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(466,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_minus ) ) @ ( A @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_1 @ ( B @ c_minus ) ) @ ( A @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
thf(2234,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) )
| ~ ( A @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(891,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less__neg_0) ).
thf(3048,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(720,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
thf(2684,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_Nat_Opower ) ) @ ( A @ ( C @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
thf(2202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_Nat_Opower ) ) @ ( A @ ( C @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(998,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(3292,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(819,axiom,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(2899,plain,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1009,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
thf(3315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(2396,plain,
c_0 != c_1,
inference(polarity_switch,[status(thm)],[2395]) ).
thf(2397,plain,
c_1 != c_0,
inference(lifteq,[status(thm)],[2396]) ).
thf(67,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
thf(1225,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
thf(2192,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(925,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
thf(3129,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(717,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
thf(2678,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(736,axiom,
! [A: $i] :
( ( c_0 != c_1 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).
thf(2720,plain,
! [A: $i] :
( ( c_0 != c_1 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(483,axiom,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
thf(2160,plain,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(814,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(2888,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(811,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
thf(2882,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(643,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
thf(2513,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( B @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_divide ) ) @ c_times ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__left_1) ).
thf(1845,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_divide ) ) @ c_times ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(858,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
thf(2977,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_Suc @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
thf(2375,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(475,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_15) ).
thf(2143,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_5) ).
thf(2012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(741,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
thf(2732,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
thf(1368,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Obin__minus @ ( c_Numeral_OPls @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(490,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_38) ).
thf(2175,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(783,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
thf(2821,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(964,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
thf(3209,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_div ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(595,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
thf(2407,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(896,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
thf(3058,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(787,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
thf(2831,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(723,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
thf(2689,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_4) ).
thf(2092,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(1432,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1020,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
thf(3344,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(605,axiom,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
thf(2429,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_plus ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_plus ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
thf(1235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_plus ) ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_plus ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
thf(1901,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less_1) ).
thf(2322,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(623,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_7) ).
thf(2468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(573,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(2354,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(706,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
thf(2656,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(879,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_8) ).
thf(3019,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(186,axiom,
! [A: $i] :
( ( ( A @ ( c_1 @ c_HOL_Oinverse ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__eq__1__iff_1) ).
thf(1499,plain,
! [A: $i] :
( ( ( A @ ( c_1 @ c_HOL_Oinverse ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__pos_1) ).
thf(1716,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
thf(2454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_Suc @ ( C @ c_minus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ ( C @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( C @ c_Numeral_Onumber__of ) @ c_plus ) ) @ c_div ) ) ) )
| ( B = c_Numeral_Obit_OB0 )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
thf(1813,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( B @ ( C @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( C @ c_Numeral_Onumber__of ) @ c_plus ) ) @ c_div ) ) ) )
| ( B = c_Numeral_Obit_OB0 )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ole__divide__eq__1__pos_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(919,axiom,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
thf(3114,plain,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(722,axiom,
tc_IntDef_Oint @ class_LOrder_Olorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(2688,plain,
tc_IntDef_Oint @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(53,axiom,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_1 )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_0) ).
thf(1188,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_1 )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_0) ).
thf(1186,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(511,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(2219,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_14) ).
thf(2128,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( B
= ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_0) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Numeral_Onumber__of ) )
= c_0 )
| ( B
= ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(924,axiom,
! [A: $i] :
( ~ ( A @ ( c_0 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
thf(3127,plain,
! [A: $i] :
( ~ ( A @ ( c_0 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_3) ).
thf(1538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(728,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(2701,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(2545,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_4) ).
thf(1738,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(888,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
thf(3041,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(661,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
thf(2558,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(277,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_IntDef_Onat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
thf(1702,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_IntDef_Onat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Omeet ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Ojoin ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Omeet ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Ojoin ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(670,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
thf(2579,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(920,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
thf(3117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(900,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = c_1 )
| ( B = c_0 )
| ( B
!= ( A @ ( C @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).
thf(3071,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_1 )
| ( B = c_0 )
| ( B
!= ( A @ ( C @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(816,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(2892,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(672,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_6) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(996,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
thf(3288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(432,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
thf(2056,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(524,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(2247,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(379,axiom,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(1934,plain,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(844,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ ( c_1 @ ( A @ c_minus ) ) @ c_Suc ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
thf(2948,plain,
! [A: $i] :
( ( A
= ( tc_nat @ ( c_1 @ ( A @ c_minus ) ) @ c_Suc ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_2) ).
thf(1766,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(916,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
thf(3107,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(923,axiom,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
thf(3124,plain,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(866,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_8) ).
thf(2992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Omeet ) ) )
= B )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
thf(1981,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Omeet ) ) )
= B )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
thf(1353,plain,
! [A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(476,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(2145,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
thf(1485,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(732,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(2711,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
thf(1585,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(642,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_45) ).
thf(2511,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
= ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
thf(1670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
= ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__divide__1__iff_1) ).
thf(1797,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(881,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
thf(3024,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(776,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(2807,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(86,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
thf(1272,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(939,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
thf(3156,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1239,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(polarity_switch,[status(thm)],[1238]) ).
thf(1240,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(lifteq,[status(thm)],[1239]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_minus ) ) @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
thf(1617,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_minus ) ) @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(338,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
thf(1839,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_minus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_minus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_4) ).
thf(1966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(813,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
!= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).
thf(2885,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
!= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__le__divide__iff__number__of_3) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(386,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(1949,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(946,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
thf(3171,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1063,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(3447,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(27,axiom,
( ( c_Numeral_Obit_OB0 @ ( c_Numeral_OPls @ c_Numeral_OBit ) )
= c_Numeral_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).
thf(1126,plain,
( ( c_Numeral_Obit_OB0 @ ( c_Numeral_OPls @ c_Numeral_OBit ) )
= c_Numeral_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(803,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_4) ).
thf(2865,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(807,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_IntDef_Oneg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
thf(2875,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_IntDef_Oneg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ c_div ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
thf(1940,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Suc @ c_Suc @ c_Suc @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_plus ) ) @ c_div ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(994,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
thf(3284,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(753,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
thf(2760,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1043,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
thf(3400,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(254,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_1) ).
thf(1649,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
thf(2352,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_1) ).
thf(2045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(909,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(3092,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(953,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(3188,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(499,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
thf(2194,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(570,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
thf(2347,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(1412,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_49) ).
thf(2215,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(193,axiom,
! [A: $i] :
( ( A = c_0 )
| ( ( A @ c_IntDef_Oint )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
thf(1517,plain,
! [A: $i] :
( ( A = c_0 )
| ( ( A @ c_IntDef_Oint )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(64,axiom,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
thf(1216,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(506,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(2209,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(746,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Omeet ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
thf(2743,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Omeet ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(869,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( B @ c_times ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
thf(2997,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( B @ c_times ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(633,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
thf(2490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(496,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_53) ).
thf(2187,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(1021,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
thf(3346,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( tc_IntDef_Oint @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(458,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
thf(2110,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1011,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= ( tc_nat @ ( B @ ( c_0 @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(3320,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= ( tc_nat @ ( B @ ( c_0 @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__eq__eq__number__of_4) ).
thf(1390,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(551,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
thf(2305,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(829,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Suc @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_1 @ c_div ) ) @ c_IntDef_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
thf(2919,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Suc @ c_div ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ ( c_1 @ c_div ) ) @ c_IntDef_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_times ) ) @ c_divide ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if2_1) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_times ) ) @ c_divide ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(895,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
thf(3056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(2226,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(2071,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(761,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
thf(2775,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_2) ).
thf(1734,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(823,axiom,
tc_IntDef_Oint @ class_Numeral_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
thf(2907,plain,
tc_IntDef_Oint @ class_Numeral_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( c_1 @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__power2_0) ).
thf(1108,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( c_1 @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(887,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
thf(3039,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(675,axiom,
tc_IntDef_Oint @ class_Power_Orecpower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(2591,plain,
tc_IntDef_Oint @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(611,axiom,
! [A: $i] :
( ( A @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
thf(2443,plain,
! [A: $i] :
( ( A @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_9) ).
thf(1326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) )
= ( c_Numeral_Obit_OB1 @ ( B @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_OBit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
thf(1253,plain,
! [B: $i,A: $i] :
( ( c_Numeral_Obit_OB0 @ ( B @ c_Numeral_OBit ) @ ( c_Numeral_Obit_OB1 @ ( A @ c_Numeral_OBit ) @ c_Numeral_Obin__add ) )
= ( c_Numeral_Obit_OB1 @ ( B @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_OBit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(536,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(545,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(2290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__0__iff_1) ).
thf(1903,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(659,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Opprt ) @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
thf(2554,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Opprt ) @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
thf(1508,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( A @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( A @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(784,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(2823,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(345,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
thf(1854,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_IntDef_Onat @ ( A @ c_IntDef_Onat @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
thf(2130,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_IntDef_Onat @ ( A @ c_IntDef_Onat @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(1030,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
thf(3368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ ( A @ ( B @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_times ) ) @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( D @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(981,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(3252,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(599,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
thf(2416,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(864,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(2988,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(677,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(2594,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(489,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(2174,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(588,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_1 )
| ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_0) ).
thf(2389,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_1 )
| ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
thf(1341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(452,axiom,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_IntDef_Oint @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
thf(2098,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_IntDef_Oint @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(265,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_6) ).
thf(1674,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_0 @ ( B @ c_divide ) ) @ ( c_0 @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__right_0) ).
thf(1639,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_0 @ ( B @ c_divide ) ) @ ( c_0 @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(779,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(2811,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(245,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
thf(1629,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(684,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Suc @ ( A @ c_Nat_Opower ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ ( A @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
thf(2608,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_Suc @ ( A @ c_Nat_Opower ) ) )
= ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_Nat_Opower ) ) @ ( A @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(975,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = c_1 )
| ( B = c_0 )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
thf(3235,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_1 )
| ( B = c_0 )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= B )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_0) ).
thf(2431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(75,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_plus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
thf(1244,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_plus ) ) )
= ( A @ c_Suc @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(755,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
thf(2764,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(837,axiom,
tc_nat @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(2934,plain,
tc_nat @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(479,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_40) ).
thf(2152,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( tc_nat @ ( B @ ( A @ c_Numeral_Obin__mult ) @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
thf(2262,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( tc_nat @ ( B @ ( A @ c_Numeral_Obin__mult ) @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(590,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(2394,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(906,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(3085,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(613,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).
thf(2447,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(183,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_HOL_Oabs ) )
= ( A @ c_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
thf(1491,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_HOL_Oabs ) )
= ( A @ c_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(443,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
thf(2081,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(501,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
thf(2198,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1023,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
thf(3351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
thf(1661,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(464,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(2120,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(2095,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_IntDef_Oneg ) ),
inference(polarity_switch,[status(thm)],[2094]) ).
thf(556,axiom,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(2315,plain,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
thf(1994,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( c_1
!= ( A @ ( C @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__eq__divide__iff_1) ).
thf(2009,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( c_1
!= ( A @ ( C @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_5) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(950,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(3181,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
thf(2384,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(627,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
thf(2475,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_div ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(766,axiom,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= B )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
thf(2786,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_div ) ) )
= B )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(703,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
thf(2648,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) @ c_IntDef_Onat ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1055,axiom,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
thf(3430,plain,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(313,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
thf(1777,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(987,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
thf(3267,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_0 @ ( B @ c_times ) ) @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if1_0) ).
thf(1294,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_0 @ ( B @ c_times ) ) @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(669,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
thf(2576,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_Numeral_OMin @ c_Numeral_Onumber__of ) @ c_times ) ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_divide ) ) @ c_divide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__divide__eq__left_0) ).
thf(2066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_divide ) ) @ c_divide ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(279,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
thf(1706,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1076,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_1 )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(cnf,[status(esa)],[1075]) ).
thf(1077,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_1 )
| ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[1076]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(718,axiom,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(2680,plain,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__eq__number__of_0) ).
thf(2183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_times ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_lessequals ) ) )
| ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
thf(1212,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_lessequals ) ) )
| ( A @ ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(516,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(2230,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_0) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_less ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__eq__number__of_3) ).
thf(1444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ c_less ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(582,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(2374,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_times ) ) )
= ( A @ ( C @ ( A @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_times ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
thf(2287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_times ) ) )
= ( A @ ( C @ ( A @ ( B @ c_Numeral_Obin__minus @ c_Numeral_Onumber__of ) @ c_times ) ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = D )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= ( A @ ( D @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__cancel__left_0) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( C = D )
| ( ( A @ ( C @ ( B @ c_divide ) ) )
!= ( A @ ( D @ ( B @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_divide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__1_0) ).
thf(1512,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_divide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(861,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(2983,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ohalf__gt__zero_0) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( c_Numeral_Obit_OB0 @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_OBit ) @ c_Numeral_Onumber__of ) @ ( B @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( A @ ( c_0 @ ( B @ c_divide ) ) @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__left_0) ).
thf(1546,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( A @ ( c_0 @ ( B @ c_divide ) ) @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(647,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
thf(2522,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( ( A @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(845,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
thf(2951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ ( A @ ( A @ ( D @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(961,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le_1) ).
thf(3203,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_minus ) ) )
= ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_minus ) ) )
= ( A @ ( c_Numeral_Obit_OB1 @ ( c_Numeral_OPls @ c_Numeral_OBit ) @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(410,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
thf(2003,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oint @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1035,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = c_1 )
| ( B = c_0 )
| ( B
!= ( A @ ( B @ ( C @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
thf(3379,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_1 )
| ( B = c_0 )
| ( B
!= ( A @ ( B @ ( C @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(835,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less__neg_1) ).
thf(2930,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(30,axiom,
( ( c_Numeral_Obit_OB1 @ ( c_Numeral_OMin @ c_Numeral_OBit ) )
= c_Numeral_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).
thf(1133,plain,
( ( c_Numeral_Obit_OB1 @ ( c_Numeral_OMin @ c_Numeral_OBit ) )
= c_Numeral_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
thf(2302,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( B @ c_plus ) ) @ c_div ) ) )
= ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_div ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
thf(2517,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ c_Numeral_Onumber__of ) )
!= c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( tc_nat @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oless__divide__eq__1__neg_0) ).
thf(1725,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( c_1 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(90,axiom,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ c_uminus ) @ ( A @ c_IntDef_Oint @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
thf(1280,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ c_uminus ) @ ( A @ c_IntDef_Oint @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
thf(1578,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(389,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( A @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
thf(1957,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( A @ c_plus ) ) )
= B )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(139,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(1395,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__less__0__iff__number__of_3) ).
thf(1625,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1032,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(3373,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(229,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
thf(1593,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(682,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__positive__iff__positive_0) ).
thf(2604,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(743,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(2736,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_times ) ) @ ( A @ ( C @ ( B @ c_times ) ) @ c_divide ) ) )
= ( A @ ( D @ ( C @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if_1) ).
thf(1986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_times ) ) @ ( A @ ( C @ ( B @ c_times ) ) @ c_divide ) ) )
= ( A @ ( D @ ( C @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(926,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
thf(3132,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_1 @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_1 @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= ( A @ ( C @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( A @ ( B @ c_Numeral_Onumber__of ) )
!= ( A @ ( C @ c_Numeral_Onumber__of ) ) )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(757,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__divide__eq__number__of_7) ).
thf(2768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).
thf(1480,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(933,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(3145,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(772,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
thf(2800,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Numeral_Onumber__of ) @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(1014,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(3328,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(404,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
thf(1989,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_plus ) ) @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_5) ).
thf(1816,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(747,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
thf(2746,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
thf(1561,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ ( A @ ( c_Numeral_OPls @ c_Numeral_Obin__minus @ ( B @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(146,axiom,
( ( c_0 @ c_IntDef_Onat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
thf(1410,plain,
( ( c_0 @ c_IntDef_Onat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(850,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(2961,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(594,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_HOL_Oinverse ) )
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oinverse__eq__divide__number__of_0) ).
thf(2404,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_HOL_Oinverse ) )
= ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_1 @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1053,axiom,
! [B: $i,A: $i] :
( ( tc_List_Ochar @ ( B @ ( A @ c_List_Ochar_OChar ) @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
thf(3426,plain,
! [B: $i,A: $i] :
( ( tc_List_Ochar @ ( B @ ( A @ c_List_Ochar_OChar ) @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(890,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
thf(3045,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(704,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Suc )
= c_1 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
thf(2651,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Suc )
= c_1 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(765,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Suc )
= ( tc_nat @ ( A @ c_Numeral_Obin__succ @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
thf(2783,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Suc )
= ( tc_nat @ ( A @ c_Numeral_Obin__succ @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(296,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
thf(1742,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( B @ c_times ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__self__right_1) ).
thf(1436,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_divide ) ) @ ( B @ c_times ) ) )
= C )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(347,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
thf(1859,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1693,plain,
~ ( tc_IntDef_Oint @ ( c_1 @ c_Parity_Oeven ) ),
inference(polarity_switch,[status(thm)],[1692]) ).
thf(513,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_Nat_Opower ) ) )
= B )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
thf(2223,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_Nat_Opower ) ) )
= B )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(770,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_56) ).
thf(2795,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(175,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_54) ).
thf(1473,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(690,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less_0) ).
thf(2619,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse ) @ c_less ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(435,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
thf(2063,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(236,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
thf(1610,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(978,axiom,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_minus ) ) @ c_Suc )
= A )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
thf(3244,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_minus ) ) @ c_Suc )
= A )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).
thf(1261,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Obin__minus @ ( A @ c_Numeral_Obin__add ) @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( c_0 @ c_times ) ) @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__left__if1_0) ).
thf(1923,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( c_0 @ c_times ) ) @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1040,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(3392,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(654,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_0) ).
thf(2539,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oiszero ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__le__0__1__iff_1) ).
thf(1299,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( c_1 @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(581,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
thf(2372,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1019,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(3341,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(482,axiom,
tc_IntDef_Oint @ class_Numeral_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
thf(2159,plain,
tc_IntDef_Oint @ class_Numeral_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1028,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(3362,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(778,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(2810,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
thf(1829,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) )
| ( tc_IntDef_Oint @ ( B @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(398,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(1977,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(774,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
thf(2803,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
thf(1532,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(794,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
thf(2847,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ozero__less__divide__iff__number__of_1) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ( A @ ( c_0 @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1047,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(3411,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(631,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
thf(2485,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1027,axiom,
! [A: $i] :
( ( A @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
thf(3360,plain,
! [A: $i] :
( ( A @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
thf(1378,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_HOL_Oinverse ) )
= ( A @ ( B @ ( C @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__divide_0) ).
thf(1582,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_HOL_Oinverse ) )
= ( A @ ( B @ ( C @ c_divide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(2265,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(984,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_times ) ) )
= ( A @ ( c_0 @ ( C @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
thf(3259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_times ) ) )
= ( A @ ( c_0 @ ( C @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( B @ c_divide ) ) )
= ( A @ ( C @ ( c_1 @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if1_1) ).
thf(1597,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( B @ c_divide ) ) )
= ( A @ ( C @ ( c_1 @ c_divide ) ) ) )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(802,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(2864,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(355,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_divide ) ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__eq__eq__1_0) ).
thf(1880,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_divide ) ) )
!= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(902,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
thf(3076,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1041,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_1 )
| ( C = c_0 )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= C )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
thf(3394,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_1 )
| ( C = c_0 )
| ( ( A @ ( C @ ( B @ c_times ) ) )
!= C )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(727,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
thf(2699,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( A @ ( c_0 @ ( B @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__divide__cancel__right__if2_0) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( A @ ( c_0 @ ( B @ c_times ) ) @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
thf(1399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
thf(1606,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_divide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__minus__right_0) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_uminus ) @ ( B @ c_divide ) ) )
= ( A @ ( A @ ( C @ ( B @ c_divide ) ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__divide__eq__number__of_6) ).
thf(1962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( D @ c_divide ) ) @ ( C @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(663,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
thf(2563,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Divides_Oop_Amod ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(965,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_times ) ) )
= ( A @ ( C @ ( c_0 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
thf(3212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_times ) ) )
= ( A @ ( C @ ( c_0 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__less__eq__1__neg_1) ).
thf(1848,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_1 @ ( A @ ( B @ ( C @ c_divide ) ) @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(149,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__self__if_0) ).
thf(1416,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ ( c_0 @ c_divide ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1056,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(3432,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ c_Parity_Oeven ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_Parity_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(616,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(2453,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odivide__le__0__iff__number__of_3) ).
thf(2106,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ( A @ ( c_0 @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( C @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_divide ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
thf(2470,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1000,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(3296,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(491,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_20) ).
thf(2177,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(810,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
thf(2879,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(699,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(2640,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ ( c_1 @ c_divide ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__divide__eq__0__iff_0) ).
thf(1653,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ ( c_1 @ c_divide ) ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(971,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(3227,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize ) )
= ( tc_nat @ ( c_0 @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
thf(1944,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize ) )
= ( tc_nat @ ( c_0 @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(911,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
thf(3096,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(505,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
thf(2206,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__minus__eq_0) ).
thf(1681,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oinverse ) )
= ( A @ ( A @ ( B @ c_HOL_Oinverse ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1045,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_IntDef_Oof__int ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
thf(3405,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_IntDef_Oof__int ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(520,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
thf(2297,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ ( A @ ( C @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( C @ ( A @ ( A @ ( B @ c_Numeral_Onumber__of ) @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Numeral_Onumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
thf(1870,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(759,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
thf(2771,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(3599,plain,
$false,
inference(e,[status(thm)],[2630,1718,2094,1823,1559,2921,3449,1818,1549,2280,1686,3021,1665,2612,1469,1168,2295,2341,2336,3008,1454,2031,3434,3167,2412,2876,2463,3397,1899,1315,1850,2499,2427,1083,2077,1750,3317,1068,2659,2527,1073,1692,3382,1173,1158,2309,2976,2808,1522,2495,2381,2395,2908,2953,1401,1422,1569,2671,1544,2676,2014,2099,2282,1591,2114,1142,1269,1793,2854,1608,1137,2686,1756,3135,3175,3338,1233,2627,3414,2042,1078,1788,1426,3004,2035,3365,2740,1999,2316,1275,2141,2434,1872,1919,2459,2901,3313,1954,2844,1222,2360,3276,2575,3370,3103,2723,2972,1914,2548,3249,2020,1359,2082,2819,1623,1887,2957,3335,1196,2985,1576,3308,1935,1650,1645,1921,1386,3281,3140,1475,2654,1709,2916,3195,1430,2039,1760,2667,2269,2755,3061,2708,1826,1313,3353,2126,2703,1287,3221,1907,2501,1330,1264,2217,1323,3148,2185,1455,2897,1191,1462,3043,2571,2356,2420,3099,2713,2169,2049,1931,1773,1362,1875,2533,2829,1892,3374,1704,1890,3014,2520,2852,3231,2007,3322,3199,1450,2090,1632,2259,3163,1151,2335,2017,2616,1946,1465,2324,1714,1373,2996,1911,2782,2451,2236,3438,2122,2925,1978,1383,2254,1960,3290,3300,3093,2777,3152,1183,2073,2861,2483,1351,2639,1201,2965,1600,1104,2718,3389,2508,1843,2058,2367,2437,1928,2618,2833,3189,1896,3421,3036,2530,1119,1622,2979,1526,2137,2103,2750,1405,2392,2154,1696,2586,1975,1564,2762,3378,1863,1074,3229,2910,2473,2118,1338,2047,3418,3011,1206,3301,2204,3169,3265,2646,1199,2364,2164,1153,3186,1311,2232,2307,3054,1067,1736,2621,2660,1768,1868,2061,2773,1636,1730,1163,2441,2589,2705,1723,2601,2249,2596,1255,1676,2147,1502,2969,3233,2606,2986,3207,1238,2560,2805,2277,1355,1580,3154,3134,1619,2150,1370,2414,2132,2890,3286,1883,3269,1365,1178,1951,1457,2200,2179,1656,2112,1573,1106,3271,2445,3191,1938,2758,3403,1968,3090,1555,2332,2826,1836,2181,2327,2213,3028,3050,2345,2211,1407,2313,1128,1634,2228,3033,3408,1740,3105,1089,1534,1804,2895,1328,1121,3218,1540,3386,3119,1762,2515,3122,2946,2990,1111,1970,1227,2692,1587,2509,1672,2858,2537,3440,3205,3087,3018,1397,1567,1493,2023,3143,3000,1292,2868,1075,2551,2666,1419,1160,2877,1964,1942,1659,1424,3441,1414,2196,2240,2172,3428,1810,1791,1214,2349,2108,1446,1612,2472,3294,1744,1478,1131,2505,2497,1984,3247,3333,1114,1324,2285,2932,1099,1297,2681,1530,2836,2487,2598,1266,2900,2387,1831,1231,2851,2243,2581,2465,2566,1799,1852,2813,2766,2052,1246,3064,1720,3109,1979,3074,3083,3201,1393,1627,2370,3215,1333,1991,2926,1241,1779,1563,2748,2963,1071,2662,1732,2634,1434,1857,1086,3225,3279,3183,2883,3173,1712,3306,2793,1663,1515,2221,2645,2189,2338,1996,1906,2001,2904,2556,1483,1273,3262,2602,1135,2729,1648,1727,1510,1251,1764,1146,1754,3358,2253,2275,2033,3257,1219,3079,1747,2941,2028,1301,1595,2734,3111,3274,1833,2727,1916,2938,3504,2791,2789,2981,1752,3081,1388,1535,1403,2716,1520,1124,2134,2959,1615,1784,3255,2525,2849,2674,2568,1795,2398,2695,1488,1139,1786,3436,1092,2166,2457,1258,3304,3355,1428,3223,2161,1707,2293,3051,3330,2738,2935,3002,2425,3416,2573,2358,2319,3101,2642,1894,1806,1524,1542,3384,1307,1175,2079,2311,1209,2119,1282,2478,2084,3238,2624,2637,2422,2284,1933,2257,1589,1603,2299,2955,2246,2669,1144,2116,2839,1771,2943,2945,3197,1801,2856,2802,3138,2378,1690,3066,1571,2871,1376,1439,2343,1630,1821,1909,3165,3006,1344,2278,2911,1688,3456,1667,1877,1471,2025,1080,2632,2610,3027,3055,1557,2780,2267,2410,2923,1149,3298,2874,2542,1460,2252,2664,2928,1381,2461,2974,3150,2842,1171,1926,2835,2086,2139,3159,3310,1496,3178,1973,2069,2770,2075,2418,1841,2439,2725,2401,1699,3423,2481,1066,1528,3241,2797,3016,2752,1775,2592,1477,3325,3142,2535,2101,1364,2967,3348,2156,1694,2693,2005,2054,3444,1809,1203,2271,3161,2037,3146,2449,1081,2333,1181,1551,2816,2914,3031,2614,2096,1304,3193,1758,1166,1467,2994,2503,1684,1277,2124,2234,3048,2684,2202,3292,2899,3376,3315,2397,1070,1225,2192,3129,2678,2720,2160,2888,2882,2513,1845,2977,2375,1156,2143,2012,2732,3462,1368,2175,2821,3209,2407,3058,2831,2689,2092,1432,3344,2429,1235,1901,2322,1679,2468,2354,2656,3019,1499,1716,2454,1813,1452,3114,2688,1188,1186,2219,2128,1317,3127,1538,2701,2545,1738,3041,2558,1702,1284,2579,3117,3071,2892,2584,3288,2056,2247,1934,2948,1766,3107,3124,2992,1981,1353,2145,1485,2711,1585,1094,2511,1670,1797,3024,2807,1272,3156,1240,1617,1839,2088,1966,2885,1553,1949,3171,3447,1126,2865,2875,1940,3284,2760,3400,3478,1649,2352,1084,2045,3092,3188,2194,2347,1412,2215,1517,1216,2209,2743,2997,1448,2490,2187,3346,2110,3320,1390,2305,2919,1289,3056,2226,2071,2775,1734,2907,1108,3039,2591,2443,1326,1253,2273,2290,1903,2554,1508,1101,2823,1854,2130,3368,3252,2416,2988,2594,2174,2389,1341,2098,1674,1639,2811,1629,2608,3235,2431,1244,2764,2934,2152,2262,2394,3085,2447,1491,2081,2198,3351,1661,2120,2095,2315,1994,2009,1861,3181,2384,2475,2786,2648,3430,1777,3267,1294,2576,2066,1706,1193,1077,2362,2680,2183,1212,2230,1309,1444,1442,2374,2287,1642,1512,2983,1097,1229,1546,2522,2951,3203,1116,2003,3379,2930,1133,2302,2517,1725,1280,1578,1957,1395,1625,3373,1593,2604,2736,1986,3132,1248,2768,1480,3145,2800,3328,1989,1816,2746,1561,1410,2961,2404,3426,3045,2651,2783,1742,1436,1859,1335,1693,2223,2795,1473,2619,1065,1346,2063,1610,3244,1261,1923,3392,2539,1299,2372,3341,2159,3362,2810,1829,1977,2803,1532,2847,1384,3411,2485,3360,1378,1582,2265,1357,3259,1597,2864,1880,3076,3394,1885,2699,1505,1399,1606,1320,1962,2563,3212,1848,1416,3432,1769,2453,2106,2470,1069,3296,2177,2879,2640,1653,3227,1944,3096,2206,1681,3405,2238,2297,1870,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA021-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.19/0.44 % Computer : n019.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 22:06:03 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/1.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.40/1.63 % [INFO] Parsing done (576ms).
% 3.40/1.64 % [INFO] Running in sequential loop mode.
% 4.96/2.15 % [INFO] eprover registered as external prover.
% 5.18/2.16 % [INFO] Scanning for conjecture ...
% 6.17/2.46 % [INFO] Found a conjecture (or negated_conjecture) and 2785 axioms. Running axiom selection ...
% 9.11/3.10 % [INFO] Axiom selection finished. Selected 1058 axioms (removed 1727 axioms).
% 10.92/3.64 % [INFO] Problem is propositional (TPTP CNF).
% 10.92/3.67 % [INFO] Type checking passed.
% 10.92/3.68 % [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 ...
% 41.14/10.22 % External prover 'e' found a proof!
% 41.14/10.22 % [INFO] Killing All external provers ...
% 41.14/10.22 % Time passed: 9565ms (effective reasoning time: 8573ms)
% 41.14/10.24 % Axioms used in derivation (1058): cls_NatSimprocs_Omult__less__cancel__right__number__of_3, cls_IntDef_Ozero__less__int__conv_0, cls_Nat_Onot__gr0_0, cls_OrderedGroup_Ojoin__0__eq__0_1, cls_Divides_Odiv__mult__self1_0, cls_Ring__and__Field_Omult__divide__cancel__right__if_0, cls_Ring__and__Field_Odivide__le__eq__1__neg_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Power_Opower__0__Suc_0, cls_NatBin_Oeq__nat__number__of_7, cls_NatArith_Oadd__diff__assoc2_0, clsrel_Ring__and__Field_Oordered__field_0, clsrel_Ring__and__Field_Oordered__field_37, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, cls_Parity_Oneq__one__mod__two_0, cls_Parity_Opower__less__zero__eq__number__of_0, cls_Ring__and__Field_Odivide__less__0__1__iff_0, cls_IntDiv_Ozdiv__zadd__self1_0, clsrel_Ring__and__Field_Oordered__idom_3, cls_NatBin_Odvd__eq__mod__eq__0__number__of_1, cls_NatBin_Oeq__nat__number__of_11, cls_IntDiv_Ozdvd__0__right_0, cls_Parity_Opower__le__zero__eq__number__of_1, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_IntArith_Oarith__special__8_0, cls_Nat_Onot__less0_0, cls_Ring__and__Field_Oinverse__less__iff__less_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_NatSimprocs_Ozero__le__divide__iff__number__of_4, cls_NatSimprocs_Ozero__less__divide__iff__number__of_4, cls_OrderedGroup_Oneg__less__iff__less_1, cls_Nat_Oone__eq__mult__iff_0, cls_List_Odrop__replicate_0, cls_IntArith_Oarith__special__7_0, cls_NatArith_Oof__nat__0__le__iff_0, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_NatBin_OSuc__pred_H_0, cls_Ring__and__Field_Ozero__eq__1__divide__iff_1, cls_NatSimprocs_Omult__less__cancel__left__number__of_5, cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0, cls_Power_Onat__zero__less__power__iff_2, clsrel_Ring__and__Field_Oordered__field_54, clsrel_Ring__and__Field_Oordered__field_48, cls_OrderedGroup_Odiff__le__0__iff__le_0, cls_Parity_Oeven__nat__power_2, cls_IntDef_Oint__eq__0__conv_1, cls_Parity_Oeven__sum_2, cls_OrderedGroup_Oneg__le__iff__le_0, cls_NatSimprocs_Oless__divide__eq__number__of_9, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Nat_Onat__add__left__cancel__less_1, cls_IntDef_Ozless__nat__conj_1, cls_NatBin_Onat__numeral__0__eq__0_0, cls_NatBin_Opower__nat__number__of__number__of_1, cls_Parity_Opower__eq__0__iff__number__of_2, cls_IntDef_Ozless__int_0, cls_NatSimprocs_Odivide__le__eq__number__of_8, cls_Ring__and__Field_Oone__divide__eq__0__iff_0, cls_Divides_Omod__eq__0D__dest_0, cls_IntDiv_Ozmod__self_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_4, cls_Ring__and__Field_Oeq__divide__eq__1_0, cls_Ring__and__Field_Oinverse__negative__iff__negative_0, cls_Nat_Onat__add__right__cancel_0, cls_Parity_Ozero__less__power__eq__number__of_4, cls_IntDef_Oof__int__0__le__iff_0, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Ofield_8, cls_Ring__and__Field_Odivide__minus__left_0, cls_Parity_Oeven__difference_2, clsarity_IntDef__Oint_52, cls_IntDiv_Ozminus__dvd__iff_1, clsarity_IntDef__Oint_24, cls_NatSimprocs_Omult__less__cancel__left__number__of_2, cls_NatSimprocs_Oeq__divide__eq__number__of_2, clsrel_Ring__and__Field_Oordered__ring__strict_26, cls_NatSimprocs_Ole__divide__eq__number__of_7, cls_OrderedGroup_Oneg__0__less__iff__less_0, cls_IntDef_Oint__nat__eq_0, cls_Set_ODiff__cancel_0, clsrel_Ring__and__Field_Oordered__idom_12, cls_Numeral_Obin__minus__0_0, cls_NatSimprocs_Ohalf__gt__zero_0, cls_Nat_Omult__le__cancel1_1, clsrel_OrderedGroup_Opordered__ab__group__add_1, cls_Parity_Oeven__nat__product_1, cls_Numeral_Onumeral__1__eq__1_0, cls_IntDiv_Ozmod__zmult__self1_0, cls_IntDef_Oof__int__0__less__iff_0, cls_NatSimprocs_Ole__divide__eq__number__of_8, cls_Nat_Oop_A_K_Omult__Suc_0, cls_Numeral_Obin__rel__simps__11_0, cls_NatSimprocs_Odivide__less__0__iff__number__of_3, cls_Binomial_Obinomial__Suc__n_0, cls_Ring__and__Field_Odivide__eq__eq__1_1, cls_NatArith_Oof__nat__0__eq__iff_1, cls_NatSimprocs_Odivide__less__eq__number__of_6, cls_Nat_Oless__one_1, clsrel_Power_Orecpower_21, clsrel_Numeral_Onumber__ring_16, cls_Parity_Oeven__nat__product_2, cls_NatSimprocs_Odivide__le__0__iff__number__of_0, cls_Divides_Odvd__refl_0, cls_NatSimprocs_Odivide__minus1_0, cls_IntDiv_Ozdiv__1_0, cls_OrderedGroup_Oneg__0__le__iff__le_1, clsrel_Ring__and__Field_Oordered__semidom_28, cls_Nat_Odiff__is__0__eq_0, cls_NatSimprocs_Ozero__less__divide__iff__number__of_0, clsrel_Ring__and__Field_Oordered__semidom_34, cls_OrderedGroup_Opprt__eq__id_0, cls_Parity_Oeven__nat__sum_1, cls_Ring__and__Field_Oinverse__eq__1__iff_1, cls_Numeral_OPls__0__eq_0, cls_OrderedGroup_Oneg__le__0__iff__le_1, cls_Nat_OSuc__Suc__eq_0, cls_IntArith_Oarith__special__11_1, cls_Nat_Oop_A_K_Omult__0_0, cls_Power_Ozero__less__power__abs__iff_2, cls_IntDiv_Ozdiv__zminus__zminus_0, clsrel_Ring__and__Field_Ofield_5, cls_Orderings_Oorder__less__irrefl_0, cls_Parity_Ozero__less__power__eq__number__of_1, cls_IntDef_Oint__Suc_0, cls_IntDiv_Ozero__less__zpower__abs__iff_2, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_NatArith_Oof__nat__less__iff_0, cls_Ring__and__Field_Oinverse__less__iff__less__neg_1, cls_NatSimprocs_Odivide__eq__eq__number__of_1, cls_Ring__and__Field_Ole__divide__eq__1__neg_0, clsarity_nat_40, clsrel_Ring__and__Field_Ofield_32, cls_Numeral_Ominus__number__of__mult_0, cls_OrderedGroup_Oabs__ge__zero_0, cls_Ring__and__Field_Oinverse__positive__iff__positive_0, cls_Numeral_Obin__succ__Pls_0, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_NatSimprocs_Ozero__less__divide__iff__number__of_5, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_IntDef_Onegative__eq__positive_0, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_List_Olist_Oinject_1, cls_NatBin_Oless__0__number__of_1, cls_NatSimprocs_Omult__less__cancel__right__number__of_2, cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0, cls_Numeral_Obin__minus__Min_0, cls_Nat_Odiff__0__eq__0_0, cls_Ring__and__Field_Ominus__mult__minus_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_IntDef_Oneg__zminus__int_0, cls_Divides_Odiv__less_0, clsrel_Ring__and__Field_Oordered__field_21, cls_Divides_Odiv__1_0, clsrel_OrderedGroup_Olordered__ab__group__join_0, cls_NatSimprocs_Odivide__le__eq__number__of_5, cls_NatBin_Oint__nat__number__of_1, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__0__eq_0, clsarity_IntDef__Oint_56, cls_IntArith_Oarith__special__10_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_Ring__and__Field_Odivide__le__0__1__iff_0, cls_IntDef_Oint__less__0__conv_0, cls_OrderedGroup_Onprt__mono_0, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, clsarity_set_2, clsarity_nat_3, cls_IntDiv_ODIVISION__BY__ZERO_0, clsrel_Numeral_Onumber__ring_12, cls_NatSimprocs_Oless__divide__eq__number__of_6, cls_Ring__and__Field_Omult__divide__cancel__left__if1_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, cls_NatSimprocs_Omult__le__cancel__left__number__of_3, cls_NatBin_Oeq__0__number__of_1, cls_NatArith_Oof__nat__less__0__iff_0, cls_OrderedGroup_Oneg__meet__eq__join_0, clsarity_IntDef__Oint_60, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_NatSimprocs_Odivide__less__0__iff__number__of_0, cls_IntDiv_Ozmod__zmult__self2_0, cls_Ring__and__Field_Omult__cancel__left1_2, cls_Numeral_Oadd__number__of__left_0, cls_List_Olength__drop_0, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Ozero__less__int__conv_1, cls_NatBin_OSuc__nat__number__of_0, cls_Numeral_Obin__rel__simps__9_0, cls_Power_Opower_Osimps__2_0, cls_Divides_Omod__add__self1_0, cls_Parity_Opower__0__left__number__of_1, cls_Power_Opower__one__right_0, cls_NatSimprocs_Oinverse__eq__divide__number__of_0, cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0, cls_IntDef_Oof__int__less__iff_0, clsarity_nat_29, cls_IntDef_Onat__le__0_0, cls_IntDiv_Odvd__zminus__iff_0, cls_NatSimprocs_Odivide__less__eq__number__of_3, cls_OrderedGroup_Odiff__le__0__iff__le_1, cls_Nat_Ozero__less__diff_1, clsrel_Numeral_Onumber__ring_23, cls_Numeral_Obin__rel__simps__2_0, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_Nat_Omult__less__cancel2_1, cls_List_Odrop__Cons__number__of_1, cls_NatSimprocs_Omult__le__cancel__right__number__of_3, clsarity_IntDef__Oint_0, cls_IntArith_Oof__int__m1_0, cls_Numeral_Omult__minus1__right_0, cls_Numeral_Obin__succ__1_0, cls_Set_OpsubsetI_0, cls_Set_Osubset__refl_0, cls_NatBin_Oeq__nat__number__of_6, cls_List_Olist_Osize__2_0, cls_NatArith_Odiff__diff__right_0, cls_Ring__and__Field_Odivide__cancel__right_1, cls_Divides_Odiv__mult__self__is__m_0, cls_NatBin_Oless__nat__number__of_2, cls_Parity_Oeven__power_2, cls_Nat_Omult__0__right_0, cls_Set_OCompl__eq__Compl__iff_0, clsrel_OrderedGroup_Opordered__ab__group__add_10, cls_IntDiv_Omod__div__trivial_0, cls_IntDiv_Ozdvd__0__left_1, cls_LOrder_Ojoin__idempotent_0, cls_Nat_Onat__add__left__cancel__le_0, clsrel_Ring__and__Field_Oordered__field_38, cls_Ring__and__Field_Omult__cancel__right1_2, cls_Power_Opower__eq__0__iff_2, cls_Ring__and__Field_Omult__divide__cancel__left__if2_1, cls_List_Odrop__Suc__Cons_0, cls_Ring__and__Field_Ofield__mult__cancel__left_1, cls_Ring__and__Field_Oinverse__eq__iff__eq_0, cls_NatSimprocs_Ole__divide__eq__number__of_0, cls_List_Olength__replicate_0, cls_Ring__and__Field_Odivide__divide__eq__left_0, cls_Ring__and__Field_Otimes__divide__self__left_1, clsrel_Ring__and__Field_Oordered__field_50, cls_OrderedGroup_Omeet__0__eq__0_0, cls_NatBin_Oless__0__number__of_0, cls_NatSimprocs_Ole__divide__eq__number__of_3, cls_NatBin_Odiv__nat__number__of_0, cls_NatSimprocs_Odivide__le__eq__number__of_3, cls_Nat_Omult__eq__1__iff_0, cls_IntDef_Onot__neg__int_0, cls_Nat_Oadd__gr__0_2, cls_IntDiv_Ozdvd__refl_0, cls_NatBin_Oeq__number__of__0_2, cls_NatArith_Oof__nat__le__iff_0, cls_NatSimprocs_Odivide__le__eq__number__of_4, cls_IntArith_Oarith__special__5_0, cls_Divides_Odiv__less__dividend_0, cls_NatSimprocs_Oless__divide__eq__number__of_2, cls_List_Ochar_Oinject_0, cls_NatSimprocs_Omod2__Suc__Suc_0, cls_Ring__and__Field_Oinverse__minus__eq_0, cls_Divides_Odvd__1__iff__1_0, cls_IntArith_Oarith__special__12_1, cls_Nat_Omult__less__cancel1_1, clsrel_OrderedGroup_Olordered__ab__group__abs_0, cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0, cls_Nat_Onat__add__left__cancel__less_0, clsrel_Numeral_Onumber__ring_5, cls_Parity_Oneg__one__even__power_0, cls_Ring__and__Field_Ominus__divide__divide_0, cls_NatBin_Odiv__nat__number__of_1, cls_NatBin_Oeq__nat__number__of_4, cls_OrderedGroup_Oabs__eq__0_0, clsarity_nat_36, cls_IntDef_Ozero__less__nat__eq_1, cls_IntArith_Oint__eq__iff__number__of_1, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, cls_IntArith_Oarith__special__17_0, clsrel_Ring__and__Field_Ofield_17, clsrel_Ring__and__Field_Oordered__field_8, cls_IntArith_Oarith__special__9_1, cls_Power_Opower__strict__increasing__iff_0, cls_Power_Ozero__le__power__abs_0, cls_Ring__and__Field_Omult__divide__cancel__right__if2_1, cls_Ring__and__Field_Odivide__cancel__left_1, cls_SetInterval_OatLeastAtMost__empty_0, cls_Power_Opower__increasing__iff_1, cls_NatSimprocs_Ole__divide__eq__number__of_4, cls_Nat_Odiff__Suc__Suc_0, cls_Nat_Omult__eq__1__iff_2, cls_Nat_Omult__le__cancel1_0, clsarity_IntDef__Oint_59, cls_IntDiv_Ozdiv__number__of__BIT_2, clsrel_Ring__and__Field_Oordered__field_49, cls_IntDef_Oof__int__le__0__iff_1, cls_Ring__and__Field_Otimes__divide__eq__2_0, cls_Nat_Oless__one_0, cls_IntDiv_Omod__mod__trivial_0, clsrel_Ring__and__Field_Oordered__semidom_35, clsarity_IntDef__Oint_47, cls_IntDef_Oint__nat__eq_1, cls_Ring__and__Field_Oinverse__positive__iff__positive_1, clsarity_IntDef__Oint_48, cls_List_Odrop__Cons__number__of_0, cls_Ring__and__Field_Odivide__less__eq__1__neg_1, cls_Ring__and__Field_Omult__divide__cancel__right__if1_0, clsarity_IntDef__Oint_19, cls_Set_Osubset__empty_0, cls_Parity_Oeven__neg_0, clsrel_OrderedGroup_Olordered__ab__group_6, cls_Parity_Ozero__less__power__nat__eq__number__of_1, cls_NatSimprocs_Oless__minus__iff__number__of_1, clsarity_IntDef__Oint_58, cls_Ring__and__Field_Oinverse__negative__iff__negative_1, cls_Ring__and__Field_Odivide__eq__0__iff_1, cls_Divides_Omod__le__divisor_0, cls_Nat_Omult__less__cancel2_0, cls_IntDiv_Opower_Osimps__2_0, cls_Parity_Oeven__nat__power_0, cls_Parity_Ozero__less__power__nat__eq__number__of_0, cls_Ring__and__Field_Omult__divide__cancel__left__if2_0, clsrel_Ring__and__Field_Oordered__idom_51, cls_Ring__and__Field_Odivide__divide__eq__right_0, cls_IntDiv_Ozdiv__minus1__right_0, cls_Power_Onat__one__le__power_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_NatSimprocs_Ominus__less__iff__number__of_1, cls_NatSimprocs_Omult__less__cancel__left__number__of_1, cls_Nat_Ole__add__diff__inverse2_0, cls_IntArith_Oarith__special__7_1, cls_Parity_Ozero__le__power__eq__number__of_1, cls_IntDef_Onegative__eq__positive_2, clsrel_Ring__and__Field_Oordered__field_60, clsrel_Ring__and__Field_Oordered__idom_38, cls_IntArith_Oarith__special__4_0, cls_IntArith_Oarith__special__10_1, clsrel_Ring__and__Field_Oordered__idom_52, cls_Divides_Odvd__0__left__iff_0, clsrel_Ring__and__Field_Oordered__field_53, clsrel_Ring__and__Field_Ofield_3, cls_Numeral_Obin__rel__simps__13_1, clsrel_OrderedGroup_Olordered__ab__group_0, cls_Parity_Oeven__product_0, cls_NatSimprocs_Omult__le__cancel__left__number__of_0, cls_Parity_Opower__le__zero__eq__number__of_5, cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1, clsrel_Ring__and__Field_Oordered__idom_36, cls_Divides_Omod__mult__self1_0, cls_Numeral_Obin__add__Pls__right_0, cls_Ring__and__Field_Odivide__le__0__1__iff_1, cls_NatSimprocs_Omult__le__cancel__left__number__of_5, clsrel_Ring__and__Field_Oordered__idom_42, cls_Power_Ozero__less__power__abs__iff_0, cls_OrderedGroup_Ozero__le__pprt_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_5, clsrel_OrderedGroup_Olordered__ab__group__join_17, cls_Nat_Oadd__is__0_1, cls_OrderedGroup_Oneg__0__less__iff__less_1, cls_Ring__and__Field_Ozero__le__divide__1__iff_0, cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0, cls_Parity_Oeven__sum_0, clsrel_Ring__and__Field_Opordered__comm__semiring_13, cls_Parity_Opower__eq__0__iff__number__of_1, cls_Parity_Oeven__nat__power_1, cls_OrderedGroup_Ojoin__0__eq__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_Power_Orecpower__class_Oaxioms__1_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0, cls_Ring__and__Field_Onot__one__le__zero_0, cls_IntDef_Oof__int__less__iff_1, cls_NatArith_Oof__nat__le__0__iff_1, cls_NatSimprocs_Odivide__less__eq__number__of_4, cls_Ring__and__Field_Odivide__le__eq__1__pos_0, cls_NatSimprocs_Omult__less__cancel__right__number__of_5, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0, cls_IntArith_Oarith__special__15_1, cls_NatBin_Oless__nat__number__of_4, cls_IntDef_Oof__int__0__le__iff_1, clsrel_Numeral_Onumber__ring_17, cls_NatArith_Oof__nat__0__less__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_36, cls_Ring__and__Field_Oinverse__le__iff__le__neg_1, cls_NatSimprocs_Oeq__divide__eq__number__of_0, cls_NatBin_Odvd__eq__mod__eq__0__number__of_0, cls_Parity_Oeven__difference_1, cls_Parity_Opower__le__zero__eq__number__of_0, cls_Set_OCompl__subset__Compl__iff_0, cls_Nat_Omult__le__cancel2_2, cls_NatSimprocs_Ozero__le__divide__iff__number__of_2, clsrel_Ring__and__Field_Oordered__idom_47, clsarity_nat_38, cls_Nat_Omult__cancel1_1, cls_OrderedGroup_Onprt__le__zero_0, cls_SetInterval_OatLeast__subset__iff_0, cls_NatBin_Oadd__nat__number__of_2, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, cls_Nat_Onat__0__less__mult__iff_0, cls_Ring__and__Field_Odivide__eq__eq__1_0, clsrel_OrderedGroup_Olordered__ab__group_17, cls_NatSimprocs_Odivide__less__eq__number__of_7, cls_Power_Ozero__less__power__abs__iff_1, cls_NatSimprocs_Omult__le__cancel__right__number__of_0, cls_NatBin_Oone__power2_0, cls_IntDef_Oof__int__eq__iff_0, clsrel_Ring__and__Field_Oordered__field_46, cls_NatArith_Oof__nat__le__0__iff_0, cls_NatSimprocs_Omod2__gr__0_1, clsrel_Ring__and__Field_Oordered__ring__strict_16, cls_Ring__and__Field_Omult__cancel__right1_1, cls_Divides_Odiv__mult__self1__is__m_0, cls_Divides_Onat__mod__div__trivial_0, cls_NatSimprocs_Ozero__le__divide__iff__number__of_5, cls_IntDiv_Ozero__less__zpower__abs__iff_1, cls_IntDiv_Odvd__zminus__iff_1, cls_NatBin_Oeq__0__number__of_2, clsrel_Ring__and__Field_Oordered__idom_18, cls_IntDef_Oof__int__0__eq__iff_0, cls_Divides_Odiv__mult__mult2_0, cls_Nat_Ole__0__eq_0, cls_Power_Opower__inject__exp_0, cls_NatArith_Odiff__less_0, cls_Divides_ODIVISION__BY__ZERO__DIV_0, cls_Numeral_Onumeral__0__eq__0_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_IntDiv_Ozdvd__triv__right_0, cls_NatBin_Omod__nat__number__of_1, cls_NatSimprocs_Omult__less__cancel__right__number__of_1, cls_Ring__and__Field_Oinverse__le__iff__le_1, cls_Nat_Ozero__less__diff_0, cls_OrderedGroup_Oneg__le__iff__le_1, cls_Set_Oempty__subsetI_0, cls_Parity_Oeven__sum_3, cls_Numeral_OMin__1__eq_0, cls_Numeral_Obin__succ__Min_0, clsarity_IntDef__Oint_31, cls_Nat_OSuc__le__mono_0, cls_IntDef_Oabs__int__eq_0, cls_Parity_Opower__le__zero__eq__number__of_4, cls_IntArith_Oarith__special__6_1, cls_Divides_Omod__add__self2_0, cls_Numeral_Obin__arith__extra__simps__2_0, cls_Divides_Odvd__0__left__iff_1, cls_Parity_Ozero__less__power__eq__number__of_3, cls_List_Odrop__0_0, cls_Ring__and__Field_Omult__eq__0__iff_0, cls_NatSimprocs_Oless__divide__eq__number__of_1, cls_IntDiv_Ozdiv__zero_0, cls_IntDiv_Opos__mod__sign_0, cls_NatBin_Oeq__nat__number__of_0, clsrel_Ring__and__Field_Oordered__field_20, cls_Parity_Oeven__nat__sum_0, cls_Power_Opower_Osimps__1_0, cls_NatBin_Oof__nat__number__of__eq_0, cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1, cls_Power_Opower__eq__0__iff_0, cls_Nat_Oone__le__mult__iff_1, clsrel_Ring__and__Field_Oordered__idom_11, cls_Ring__and__Field_Odivide__eq__0__iff_2, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_Ring__and__Field_Omult__cancel__left1_1, cls_List_Olist_Oinject_0, clsrel_OrderedGroup_Olordered__ab__group__meet_6, cls_NatSimprocs_Oadd__2__eq__Suc_H_0, cls_Nat_OSuc__less__eq_1, cls_IntArith_Oarith__special__14_0, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsrel_Ring__and__Field_Oordered__field_42, cls_Set_Oempty__Diff_0, clsarity_nat_37, cls_NatSimprocs_Odivide__eq__eq__number__of_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_15, cls_IntArith_Oarith__special__9_0, cls_IntDef_Oint__int__eq_0, clsrel_LOrder_Olorder_0, cls_Divides_Omod__mult__self1__is__0_0, cls_Orderings_Oorder__less__imp__le_0, cls_Parity_Opower__0__left__number__of_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Numeral_Obin__rel__simps__13_0, cls_IntDiv_Ozdvd__triv__left_0, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, cls_Parity_Oeven__nat__zero_0, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1, cls_NatSimprocs_Odivide__less__0__iff__number__of_1, cls_Divides_Omod__less__divisor_0, cls_Nat_Omult__cancel2_0, cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0, clsarity_set_14, cls_Nat_Omult__less__cancel1_0, cls_Ring__and__Field_Ozero__le__one_0, cls_Set_Osubset__antisym_0, cls_IntArith_Oarith__special__8_1, clsrel_Ring__and__Field_Oordered__semidom_12, cls_Ring__and__Field_Omult__cancel__left2_0, cls_Parity_Oeven__power_1, cls_Power_Opower__strict__increasing__iff_1, cls_NatSimprocs_Oless__divide__eq__number__of_5, cls_IntDef_Ozless__nat__conj_2, cls_Numeral_Obin__add__BIT__10_0, cls_NatBin_Oint__nat__number__of_0, cls_NatSimprocs_Odivide__le__eq__number__of_9, cls_IntDiv_Ozdvd__1__left_0, clsrel_Numeral_Onumber__ring_30, clsarity_IntDef__Oint_37, cls_Ring__and__Field_Omult__divide__cancel__right__if2_0, cls_Ring__and__Field_Ole__divide__eq__1__pos_0, cls_Ring__and__Field_Oone__eq__divide__iff_1, clsarity_nat_6, cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0, cls_NatSimprocs_Oright__diff__distrib__number__of_0, clsarity_nat_43, cls_IntDef_Onegative__eq__positive_1, clsrel_Ring__and__Field_Oordered__field_31, cls_IntDiv_Ozdiv__number__of__BIT_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_2, cls_NatBin_Oeq__nat__number__of_10, cls_Divides_Omod__1_0, cls_Numeral_Obin__arith__extra__simps__4_0, clsrel_OrderedGroup_Olordered__ab__group__abs_16, clsrel_Power_Orecpower_3, cls_Set_Osubset__empty_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0, cls_Numeral_Obin__add__Pls_0, cls_Ring__and__Field_Oinverse__less__iff__less__neg_0, cls_Ring__and__Field_Odivide__eq__0__iff_0, clsrel_OrderedGroup_Olordered__ab__group__meet_15, cls_IntDiv_Ozmod__zero_0, cls_NatSimprocs_Omod2__gr__0_0, cls_Nat_OSuc__diff__diff_0, cls_OrderedGroup_Opprt__0_0, cls_Ring__and__Field_Ozero__le__divide__1__iff_1, cls_Nat_Omult__cancel2_1, cls_IntArith_Oone__less__nat__eq_1, cls_Finite__Set_Oof__nat__id_0, cls_NatBin_Oeq__nat__number__of_5, cls_NatBin_Omod__nat__number__of_2, clsarity_IntDef__Oint_18, clsrel_OrderedGroup_Olordered__ab__group__join_8, cls_IntArith_Oint__eq__iff__number__of_0, cls_Nat_Onat__0__less__mult__iff_1, cls_NatSimprocs_Ole__divide__eq__number__of_1, cls_Ring__and__Field_Otimes__divide__eq__1_0, cls_NatSimprocs_Ominus__less__iff__number__of_0, clsarity_nat_34, cls_Parity_Ozero__less__power__nat__eq__number__of_2, cls_Ring__and__Field_Oabs__divide_0, clsrel_Ring__and__Field_Oordered__idom_46, cls_NatSimprocs_Odivide__le__eq__number__of_2, cls_Ring__and__Field_Ozero__less__divide__1__iff_1, cls_Binomial_Obinomial__n__n_0, clsrel_Ring__and__Field_Oordered__semidom_38, cls_Ring__and__Field_Oless__divide__eq__1__neg_0, clsarity_nat_45, cls_NatSimprocs_Odiv__Suc__eq__div__add3_0, cls_IntDiv_Ozdiv__number__of__BIT_1, cls_Nat_OSuc__le__mono_1, clsrel_Ring__and__Field_Oordered__ring__strict_35, cls_Ring__and__Field_Omult__minus__left_0, cls_NatSimprocs_Omult__le__cancel__right__number__of_5, cls_NatBin_Omult__nat__number__of_0, cls_IntDef_Oof__int__less__0__iff_0, cls_OrderedGroup_Opprt__eq__0_0, cls_NatBin_Onat__number__of_0, cls_SetInterval_OatLeastLessThan__empty_0, cls_NatBin_Oless__nat__number__of_3, clsrel_Ring__and__Field_Oordered__semidom_36, cls_Divides_Omod__mult__self2_0, cls_Numeral_Obin__add__BIT__11_0, cls_OrderedGroup_Oabs__of__nonpos_0, cls_NatArith_Odiff__Suc__diff__eq2_0, cls_Binomial_Obinomial__Suc__Suc_0, cls_Ring__and__Field_Oless__divide__eq__1__pos_1, clsarity_nat_17, cls_NatSimprocs_Odivide__less__0__iff__number__of_5, cls_Ring__and__Field_Omult__divide__cancel__left__if1_1, cls_Ring__and__Field_Odivide__cancel__left_0, cls_NatSimprocs_Odivide__less__eq__number__of_0, cls_Numeral_Obin__rel__simps__4_0, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1, cls_NatSimprocs_Oeq__divide__eq__number__of_4, cls_IntDiv_Ozdiv__zmult__self1_0, cls_NatSimprocs_Omult__le__cancel__right__number__of_2, cls_Divides_Odvd__triv__right_0, cls_Ring__and__Field_Oinverse__divide_0, clsrel_Ring__and__Field_Oordered__field_56, cls_NatSimprocs_Ozero__less__divide__iff__number__of_2, cls_Numeral_Obin__arith__extra__simps__5_0, cls_IntArith_Ozle__add1__eq__le_1, cls_NatArith_Oof__nat__0__less__iff_0, cls_NatBin_Oadd__nat__number__of_1, cls_OrderedGroup_Opprt__mono_0, cls_IntDef_Onat__int_0, cls_OrderedGroup_Odiff__less__0__iff__less_0, cls_Ring__and__Field_Oright__inverse_0, cls_NatSimprocs_Odivide__less__eq__number__of_5, clsarity_IntDef__Oint_54, clsrel_Ring__and__Field_Oordered__field_58, clsrel_LOrder_Ojoin__semilorder_1, cls_Nat_Odiff__is__0__eq_H_0, clsarity_IntDef__Oint_40, cls_Ring__and__Field_Ole__divide__eq__1__pos_1, cls_Ring__and__Field_Odivide__less__eq__1__neg_0, clsrel_Numeral_Onumber__ring_22, cls_List_Oreplicate_Oreplicate__Suc_0, cls_Parity_Oeven__nat__Suc_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, cls_Nat_Oadd__gr__0_0, cls_IntArith_Ozabs__less__one__iff_0, cls_Parity_Oneg__one__odd__power_0, clsrel_Ring__and__Field_Oordered__idom_53, cls_OrderedGroup_Odiff__less__0__iff__less_1, clsrel_OrderedGroup_Olordered__ab__group__join_16, cls_NatBin_Oone__mod__nat__number__of_0, cls_Ring__and__Field_Oeq__divide__eq__1_2, clsrel_Ring__and__Field_Oordered__idom_35, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_IntArith_Oarith__special__13_0, cls_Nat_Oless__Suc0_0, cls_NatBin_Oeq__nat__number__of_9, cls_IntDef_Oint__1_0, cls_NatSimprocs_Ozero__le__divide__iff__number__of_1, cls_NatArith_Oof__nat__eq__0__iff_0, cls_Divides_Odvd__triv__left_0, cls_NatSimprocs_Ole__divide__eq__number__of_5, cls_OrderedGroup_Oabs__minus__cancel_0, cls_NatBin_Oof__nat__number__of__eq_1, cls_IntArith_Oarith__special__16_1, cls_Numeral_Obin__rel__simps__6_1, cls_Nat_Oop_A_N_Odiff__0_0, cls_Parity_Opower__less__zero__eq__number__of_2, cls_OrderedGroup_Onprt__eq__0_0, cls_Parity_Oeven__difference_0, cls_Ring__and__Field_Odivide__1_0, cls_Parity_Opower__le__zero__eq__number__of_3, cls_Numeral_Obin__rel__simps__7_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_IntArith_Ozle__diff1__eq_0, cls_Numeral_Obin__arith__extra__simps__3_0, cls_NatBin_Onat__numeral__1__eq__1_0, clsrel_LOrder_Olorder_2, cls_Nat_Onot__add__less1_0, cls_Parity_Oodd__one_0, cls_Divides_Odvd__0__right_0, cls_IntDef_Onot__zle__0__negative_0, cls_OrderedGroup_Ozero__less__abs__iff_1, cls_SetInterval_OatLeast__subset__iff_1, clsrel_Ring__and__Field_Oordered__field_52, clsrel_OrderedGroup_Olordered__ab__group__abs_1, clsrel_Ring__and__Field_Oordered__ring__strict_24, cls_NatArith_Odiff__diff__cancel_0, cls_NatSimprocs_Omult__le__cancel__left__number__of_1, cls_Nat_Oadd__is__0_2, cls_OrderedGroup_Oabs__eq__0_1, cls_Ring__and__Field_Omult__cancel__left1_0, cls_Numeral_Oadd__number__of__diff2_0, clsrel_Ring__and__Field_Oordered__field_34, cls_NatBin_Omod__nat__number__of_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, cls_NatSimprocs_Odivide__less__eq__number__of_9, cls_Parity_Oeven__nat__sum_2, cls_NatBin_Opower2__eq__square__number__of_0, clsrel_OrderedGroup_Olordered__ab__group_15, cls_NatSimprocs_Omult__le__cancel__left__number__of_4, clsrel_Ring__and__Field_Oordered__idom_41, cls_Ring__and__Field_Otimes__divide__self__right_1, cls_IntDef_Onot__int__zless__negative_0, clsrel_Ring__and__Field_Oordered__ring__strict_28, cls_Ring__and__Field_Onot__one__less__zero_0, cls_NatBin_Oeq__number__of__0_0, cls_Parity_Oeven__product_1, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_Nat_Omult__cancel1_0, cls_Parity_Ozero__less__power__eq__number__of_2, cls_NatSimprocs_Oless__divide__eq__number__of_0, clsrel_Ring__and__Field_Oordered__field_14, clsarity_IntDef__Oint_32, cls_IntDiv_Ozmod__zadd__self2_0, cls_NatSimprocs_Ole__minus__iff__number__of_1, cls_Parity_Oeven__power_0, cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0, cls_List_Onot__Cons__self_0, cls_Ring__and__Field_Omult__divide__cancel__left__if_1, clsarity_IntDef__Oint_22, cls_IntArith_Oarith__special__14_1, clsrel_Ring__and__Field_Oring_12, cls_Nat_Omult__le__cancel2_1, clsrel_Ring__and__Field_Oordered__field_47, cls_Nat_Oone__eq__mult__iff_2, cls_Ring__and__Field_Oless__divide__eq__1__pos_0, cls_Nat_Odiff__Suc__less_0, cls_Numeral_Obin__rel__simps__4_1, cls_NatSimprocs_Odivide__le__eq__number__of_7, cls_NatBin_Oless__nat__number__of_0, cls_OrderedGroup_Oabs__le__zero__iff_0, cls_Ring__and__Field_Oone__neq__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_2, cls_Nat_OOne__nat__def_0, cls_IntDiv_Oneg__mod__bound_0, cls_OrderedGroup_Oneg__less__0__iff__less_1, clsrel_Ring__and__Field_Oordered__ring__strict_3, cls_Nat_Oadd__0__right_0, cls_Nat_Ole__add__diff__inverse_0, cls_NatSimprocs_Odivide__less__0__iff__number__of_2, cls_Ring__and__Field_Omult__zero__right_0, clsarity_nat_5, cls_IntArith_Oarith__special__3_0, cls_Binomial_Obinomial__n__0_0, cls_Numeral_Obin__arith__extra__simps__6_1, cls_Nat_Onot__gr0_1, cls_Numeral_Obin__rel__simps__6_0, cls_Set_ODiff__eq__empty__iff_1, cls_Nat_Onot__add__less2_0, cls_Power_Onat__zero__less__power__iff_1, cls_NatSimprocs_Oless__divide__eq__number__of_4, cls_IntArith_Oarith__special__2_0, cls_NatBin_Oeq__nat__number__of_1, cls_NatBin_Ozero__power2_0, cls_Ring__and__Field_Oabs__inverse_0, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_Set_ODiff__eq__empty__iff_0, cls_Set_OpsubsetE_0, cls_IntDiv_Oneg__mod__sign_0, clsrel_Ring__and__Field_Oordered__field_45, clsrel_Ring__and__Field_Oordered__idom_8, cls_Nat_Oadd__Suc__right_0, cls_IntDiv_Ozero__less__zpower__abs__iff_0, cls_NatArith_Oof__nat__eq__0__iff_1, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, cls_NatSimprocs_Odivide__eq__eq__number__of_4, clsrel_Ring__and__Field_Oordered__semidom_26, cls_IntDef_Ozless__int_1, cls_Set_ODiff__empty_0, clsrel_Ring__and__Field_Oordered__idom_40, cls_Numeral_Obin__rel__simps__12_0, cls_Numeral_Obin__rel__simps__1_1, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, cls_NatArith_Oof__nat__eq__iff_0, cls_Ring__and__Field_Oabs__one_0, cls_Ring__and__Field_Oinverse__le__iff__le_0, cls_Ring__and__Field_Ole__divide__eq__1__neg_1, clsarity_nat_9, cls_Ring__and__Field_Omult__cancel__right2_0, cls_IntDiv_Ozmod__eq__0D__dest_0, clsarity_set_13, cls_Numeral_Obit_Odistinct__1_0, cls_Numeral_Obin__mult__Pls_0, cls_Numeral_Obin__mult__0_0, cls_Numeral_Omult__minus1_0, cls_NatSimprocs_Oless__minus__iff__number__of_0, cls_IntArith_Oarith__special__15_0, cls_Ring__and__Field_Odivide__minus__right_0, cls_Ring__and__Field_Ofield__mult__cancel__right_0, cls_IntDef_Oof__int__eq__0__iff_0, cls_NatSimprocs_Ozero__less__divide__iff__number__of_3, cls_NatSimprocs_Omult__less__cancel__right__number__of_0, clsrel_Ring__and__Field_Oordered__ring__strict_0, cls_NatArith_Odiff__Suc__diff__eq1_0, cls_Numeral_Obin__mult__1_0, cls_Nat_Oone__le__mult__iff_0, cls_Ring__and__Field_Ofield__mult__cancel__right_1, cls_Ring__and__Field_Otimes__divide__self__left_0, clsrel_OrderedGroup_Olordered__ab__group_8, clsrel_Ring__and__Field_Oordered__semidom_5, cls_Parity_Oneq__one__mod__two_1, cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1, cls_IntArith_Oarith__special__13_1, cls_Parity_Opower__le__zero__eq__number__of_2, cls_NatSimprocs_Odivide__less__eq__number__of_1, cls_Numeral_Omult__number__of__left_0, cls_Divides_Omod__less_0, cls_Parity_Oeven__zero_0, cls_IntArith_Ozabs__less__one__iff_1, cls_NatSimprocs_Oless__divide__eq__number__of_8, cls_Parity_Oeven__sum_1, cls_OrderedGroup_Oneg__less__iff__less_0, clsarity_nat_46, cls_Nat_Odiff__diff__left_0, cls_Ring__and__Field_Omult__nonneg__nonneg_0, cls_Parity_Ozero__less__power__eq__number__of_5, cls_IntDef_Ozero__zle__int_0, cls_NatArith_Oadd__diff__assoc_0, cls_IntArith_Oarith__special__1_0, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__semidom_6, cls_Parity_Ozero__le__power__eq__number__of_0, cls_Ring__and__Field_Omult__divide__cancel__left__if_0, clsrel_Ring__and__Field_Ofield_11, clsrel_Ring__and__Field_Oordered__ring__strict_34, cls_Parity_Opower__less__zero__eq__number__of_1, cls_Binomial_Obinomial__1_0, cls_Ring__and__Field_Odivide__less__0__1__iff_1, cls_Ring__and__Field_Odivide__less__eq__1__pos_1, cls_Ring__and__Field_Oinverse__mult__distrib_0, cls_Numeral_Obin__arith__extra__simps__1_0, clsrel_Ring__and__Field_Oordered__idom_44, cls_IntArith_Onat__1_0, cls_IntDef_Oof__int__le__iff_1, cls_Divides_Odiv__mult__mult1_0, cls_OrderedGroup_Oabs__0__eq_1, cls_Ring__and__Field_Oinverse__eq__1__iff_0, cls_IntDiv_Ozmod__minus1__right_0, cls_NatSimprocs_Oeq__divide__eq__number__of_3, cls_IntDef_Oof__int__0__less__iff_1, cls_Orderings_Oorder__class_Oaxioms__1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_0, cls_Ring__and__Field_Omult__divide__cancel__right__if_1, cls_OrderedGroup_Onprt__0_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, cls_NatSimprocs_Odivide__le__0__iff__number__of_1, cls_Power_Opower__eq__0__iff_1, cls_NatSimprocs_Ozero__le__divide__iff__number__of_3, cls_IntDiv_Ozdiv__zadd__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_20, cls_NatBin_Omult__nat__number__of_1, cls_Divides_Omod__self_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Power_Orecpower_9, cls_NatSimprocs_Ole__divide__eq__number__of_6, clsrel_Ring__and__Field_Oordered__ring__strict_18, clsrel_OrderedGroup_Olordered__ab__group_2, cls_IntDef_Oof__int__less__0__iff_1, cls_IntDef_Ozle__int_1, cls_Divides_Odiv__mult__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_23, cls_NatSimprocs_Omult__less__cancel__left__number__of_4, cls_Divides_Odiv__0_0, cls_NatSimprocs_Ozero__less__divide__iff__number__of_1, clsrel_Ring__and__Field_Oordered__ring__strict_29, cls_IntDef_Oof__int__le__0__iff_0, cls_Nat_OSuc__not__Zero_0, cls_NatSimprocs_Omult__less__cancel__right__number__of_4, clsrel_OrderedGroup_Opordered__ab__group__add_13, cls_Nat_Omult__less__cancel1_2, clsrel_OrderedGroup_Olordered__ab__group__abs_17, cls_Nat_Oless__Suc0_1, cls_IntDef_Oint__eq__0__conv_0, cls_IntDiv_Ozero__le__zpower__abs_0, cls_IntDiv_Ozdiv__self_0, cls_Divides_Odvd__1__left_0, cls_NatSimprocs_Odivide__le__eq__number__of_1, cls_SetInterval_OatMost__subset__iff_0, cls_Numeral_Obin__rel__simps__3_0, clsrel_Ring__and__Field_Oordered__semidom_29, cls_NatBin_Oeq__nat__number__of_2, cls_Parity_Oeven__nat__Suc_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, cls_NatSimprocs_Odivide__less__0__iff__number__of_4, cls_IntArith_Oarith__special__6_0, cls_Ring__and__Field_Odivide__eq__eq__1_2, clsrel_Ring__and__Field_Oordered__field_6, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0, cls_NatSimprocs_Omult__less__cancel__left__number__of_3, cls_NatSimprocs_Ozero__le__divide__iff__number__of_0, cls_NatSimprocs_Omod__Suc__eq__mod__add3_0, cls_Divides_ODIVISION__BY__ZERO__MOD_0, cls_Nat_Onat__add__left__cancel_0, cls_IntDef_Oof__int__0__eq__iff_1, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, cls_IntDef_Onegative__zle_0, clsarity_nat_13, cls_Ring__and__Field_Oeq__divide__eq__1_1, cls_Ring__and__Field_Odivide__le__eq__1__pos_1, cls_Ring__and__Field_Omult__zero__left_0, cls_Ring__and__Field_Omult__divide__cancel__right__if1_1, cls_NatArith_Oof__nat__less__iff_1, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_Numeral_Onumber__ring_21, cls_NatSimprocs_Oadd__2__eq__Suc_0, cls_NatSimprocs_Oadd__self__div__2_0, cls_IntDiv_Ozdiv__zmult__self2_0, cls_Divides_Onat__mod__mod__trivial_0, cls_Ring__and__Field_Omult__cancel__right1_0, cls_Nat_Oone__le__mult__iff_2, cls_Numeral_Obin__add__BIT__0_0, clsarity_IntDef__Oint_41, cls_Numeral_Obin__minus__Pls_0, cls_NatSimprocs_Odivide__le__0__iff__number__of_3, cls_Power_Opower__one_0, cls_Parity_Oeven__nat__product_0, cls_IntArith_Ozle__add1__eq__le_0, clsarity_nat_24, cls_IntArith_Oarith__special__16_0, cls_NatBin_OSuc__nat__number__of_1, cls_OrderedGroup_Oneg__le__0__iff__le_0, clsrel_Ring__and__Field_Oordered__idom_34, cls_NatBin_Oeq__nat__number__of_8, cls_NatSimprocs_Ole__divide__eq__number__of_2, cls_NatSimprocs_Omult__less__cancel__left__number__of_0, cls_Parity_Ozero__less__power__eq__number__of_0, cls_NatSimprocs_Omult__le__cancel__right__number__of_1, clsrel_Ring__and__Field_Oordered__field_51, cls_Ring__and__Field_Oless__divide__eq__1__neg_1, cls_NatBin_Oone__mod__nat__number__of_1, clsrel_OrderedGroup_Olordered__ab__group__join_15, cls_NatSimprocs_Ominus__le__iff__number__of_0, cls_List_Olexn_Osimps__1_0, clsrel_LOrder_Omeet__semilorder_1, clsarity_set_0, clsarity_IntDef__Oint_51, cls_IntArith_Ozle__diff1__eq_1, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_IntDiv_Ozminus__dvd__iff_0, cls_Ring__and__Field_Oinverse__less__iff__less_1, cls_Nat_Ole0_0, cls_Nat_OSuc__less__eq_0, cls_Parity_Oeven__nat__sum_3, cls_Parity_Opower__eq__0__iff__number__of_0, cls_NatSimprocs_Odiv2__Suc__Suc_0, clsarity_nat_4, cls_OrderedGroup_Oneg__0__le__iff__le_0, cls_Ring__and__Field_Odivide__less__eq__1__pos_0, cls_NatBin_Oone__div__nat__number__of_0, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Olordered__ab__group__meet_8, cls_NatSimprocs_Odivide__less__eq__number__of_2, clsarity_IntDef__Oint_63, cls_IntDiv_Opower_Osimps__1_0, cls_IntDef_Oint__0__neq__1_0, cls_NatSimprocs_Oless__divide__eq__number__of_7, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0, cls_IntArith_Oone__less__nat__eq_0, cls_NatSimprocs_Odivide__eq__eq__number__of_0, cls_NatBin_Oadd__nat__number__of_0, cls_IntDef_Ozless__nat__conj_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Numeral_Obin__succ__0_0, cls_Ring__and__Field_Odivide__le__eq__1__neg_1, cls_Parity_Oeven__difference_3, clsrel_Ring__and__Field_Oordered__semidom_30, cls_IntDiv_Opos__mod__bound_0, cls_Ring__and__Field_Odivide__self__if_0, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_Nat_Oadd__gr__0_1, cls_Ring__and__Field_Oinverse__le__iff__le__neg_0, cls_Set_Onot__psubset__empty_0, cls_Numeral_Obin__arith__extra__simps__6_0, cls_Numeral_Obin__rel__simps__1_0, cls_NatSimprocs_Ominus__le__iff__number__of_1, cls_NatSimprocs_Odivide__less__eq__number__of_8, cls_NatArith_Oof__nat__0__eq__iff_0, cls_IntArith_Oabs__minus__one_0, clsarity_IntDef__Oint_50, cls_Ring__and__Field_Odivide__cancel__right_0, cls_Nat_Omult__le__cancel1_2, cls_NatSimprocs_Ole__minus__iff__number__of_0, cls_NatSimprocs_Ominus1__divide_0, clsrel_Power_Orecpower_16, cls_IntDef_Ozero__less__nat__eq_0, cls_OrderedGroup_Oneg__less__0__iff__less_0, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, cls_SetInterval_OgreaterThanAtMost__empty_0, cls_NatBin_Oeq__nat__number__of_3, cls_Nat_Ole__0__eq_1, cls_IntArith_Oint__eq__iff__number__of_2, clsrel_Ring__and__Field_Oordered__field_40, cls_List_Ochar_Oinject_1, cls_NatSimprocs_Omult__le__cancel__left__number__of_2, cls_OrderedGroup_Oabs__of__nonneg_0, clsrel_Ring__and__Field_Oordered__field_15, cls_Numeral_Obin__rel__simps__5_0, cls_Power_Opower__increasing__iff_0, cls_NatSimprocs_Ole__divide__eq__number__of_9, cls_Divides_Odiv__le__dividend_0, cls_Numeral_Obin__rel__simps__12_1, cls_Parity_Oeven__product_2, cls_Nat_Oop_A_L_Oadd__Suc_0, cls_Ring__and__Field_Oinverse__inverse__eq_0, clsrel_Ring__and__Field_Ofield_18, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Set_OpsubsetE_1, cls_Nat_Omult__le__cancel2_0, cls_NatSimprocs_Oleft__diff__distrib__number__of_0, clsarity_IntDef__Oint_55, cls_NatSimprocs_Odivide__le__eq__number__of_0, clsrel_OrderedGroup_Olordered__ab__group__meet_2, cls_IntDiv_Ozmod__zminus__zminus_0, cls_Nat_OZero__not__Suc_0, cls_Divides_Omod__mult__self__is__0_0, cls_SetInterval_OatMost__subset__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_2, cls_Nat_OlessI_0, cls_IntDef_Oof__int__eq__0__iff_1, cls_OrderedGroup_Oabs__idempotent_0, cls_Set_Odouble__complement_0, cls_Divides_Odiv__self_0, cls_NatBin_Oless__nat__number__of_1, cls_NatSimprocs_Odivide__le__eq__number__of_6, cls_OrderedGroup_Oabs__le__zero__iff_1, cls_Ring__and__Field_Ozero__less__divide__1__iff_0, cls_Ring__and__Field_Ozero__eq__1__divide__iff_0, cls_NatSimprocs_Oless__divide__eq__number__of_3, cls_Nat_Omult__less__cancel2_2, cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0, cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1, cls_Nat_OSuc__pred_0, cls_IntArith_Oabs__power__minus__one_0, clsrel_Ring__and__Field_Oordered__ring__strict_30, cls_Ring__and__Field_Odivide__eq__1__iff_1, cls_IntDef_Onat__zero_0, cls_IntDiv_Ozdvd__0__left_0, cls_Nat_Omult__eq__1__iff_1, cls_NatBin_Oeq__nat__number__of_12, cls_NatBin_Oeq__number__of__0_1, cls_NatSimprocs_Omult__le__cancel__right__number__of_4, cls_Divides_Omod__0_0, cls_Nat_Omult__Suc__right_0, cls_Ring__and__Field_Ofield__mult__cancel__left_0, cls_Ring__and__Field_Omult__minus__right_0, cls_IntDef_Oint__le__0__conv_0, cls_Nat_Oone__eq__mult__iff_1, cls_List_Ochar_Osize_0, clsrel_Ring__and__Field_Ofield_12, cls_NatArith_Oof__nat__le__iff_1, cls_OrderedGroup_Omeet__0__eq__0_1, cls_Numeral_Obit_Odistinct__2_0, cls_OrderedGroup_Oneg__join__eq__meet_0, cls_IntDef_Onat__zminus__int_0, cls_Nat_Omult__is__0_0, cls_IntDiv_Ozmod__zadd__self1_0, cls_Ring__and__Field_Otimes__divide__self__right_0, cls_Parity_Ozero__le__power__eq__number__of_2, cls_IntDef_Oint__le__0__conv_1, cls_IntArith_Oarith__special__17_1, cls_Parity_Opower__even__abs__number__of_0, clsrel_Ring__and__Field_Oordered__field_11, cls_Parity_Oeven__neg_1, cls_IntDef_Onegative__zless_0, cls_Numeral_Obin__mult__Min_0, cls_NatBin_Oeq__0__number__of_0, cls_Power_Onat__zero__less__power__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_18, cls_IntArith_Oarith__special__12_0, clsrel_Ring__and__Field_Oring_7, cls_IntDiv_Ozmod__1_0, cls_Divides_Odvd__1__iff__1_1, cls_IntArith_Oarith__special__11_0, cls_Ring__and__Field_Oone__divide__eq__0__iff_1, cls_Binomial_Obinomial__0__Suc_0, cls_IntDef_Ozle__int_0, clsarity_IntDef__Oint_9, clsarity_set_15, cls_List_Odrop__drop_0
% 41.14/10.24 % No. of inferences in proof: 2160
% 41.14/10.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9565 ms resp. 8573 ms w/o parsing
% 41.47/10.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 41.47/10.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------