%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA045-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 06:50:23 AM UTC 2026
% Result : Unsatisfiable 14.49s 4.73s
% Output : Refutation 15.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 527
% Syntax : Number of formulae : 1055 ( 285 unt; 0 typ; 0 def)
% Number of atoms : 2167 ( 578 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 8784 (1046 ~;1112 |; 0 &;6626 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 61 usr; 8 con; 0-3 aty)
% Number of variables : 1680 ( 0 ^;1680 !; 0 ?;1680 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_IntDef_Oint_decl,type,
c_IntDef_Oint: $i > $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $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(c_Nat_Opower_decl,type,
c_Nat_Opower: $i > $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_IntDef_Oneg_decl,type,
c_IntDef_Oneg: $i > $i > $o ).
thf(c_Numeral_Onumber__of_decl,type,
c_Numeral_Onumber__of: $i > $i > $i ).
thf(c_Divides_Oop_Amod_decl,type,
c_Divides_Oop_Amod: $i > $i > $i > $i ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(c_div_decl,type,
c_div: $i > $i > $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
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(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(c_1_decl,type,
c_1: $i ).
thf(class_Power_Orecpower_decl,type,
class_Power_Orecpower: $i > $o ).
thf(c_Parity_Oeven_decl,type,
c_Parity_Oeven: $i > $i > $o ).
thf(c_IntDef_Onat_decl,type,
c_IntDef_Onat: $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $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_Opordered__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__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__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(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__meet_decl,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
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_OrderedGroup_Olordered__ab__group__join_decl,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__abs__if_decl,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
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_OrderedGroup_Opprt_decl,type,
c_OrderedGroup_Opprt: $i > $i > $i ).
thf(c_HOL_Oinverse_decl,type,
c_HOL_Oinverse: $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(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Ochar_decl,type,
tc_List_Ochar: $i ).
thf(516,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_IntDef_Oof__int ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
thf(1665,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)],[516]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(1337,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)],[368]) ).
thf(404,axiom,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(1411,plain,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(434,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(1469,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(383,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(1369,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)],[383]) ).
thf(104,axiom,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
thf(760,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(504,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(1633,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)],[504]) ).
thf(474,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(1559,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(359,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(1315,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
thf(941,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)],[183]) ).
thf(297,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(1179,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
thf(777,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)],[111]) ).
thf(470,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
thf(1549,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)],[470]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
thf(1110,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
thf(1501,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)],[449]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(809,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)],[125]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(628,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)],[45]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
thf(1031,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)],[227]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
thf(1200,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)],[307]) ).
thf(401,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(1406,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(346,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(1290,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(244,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(1068,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(458,axiom,
! [A: $i] :
( ~ ( A @ ( c_0 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
thf(1522,plain,
! [A: $i] :
( ~ ( A @ ( c_0 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(208,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(994,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(478,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
thf(1569,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)],[478]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
thf(1205,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)],[309]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ ( c_1 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
thf(1591,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)],[486]) ).
thf(527,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(1692,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(1158,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)],[288]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
thf(582,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)],[22]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
thf(762,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)],[105]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
thf(1142,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)],[280]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_1) ).
thf(1269,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)],[336]) ).
thf(353,axiom,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(1305,plain,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(597,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)],[29]) ).
thf(494,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(1608,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)],[494]) ).
thf(278,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
thf(1137,plain,
c_0 != c_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(320,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
thf(1233,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)],[320]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(814,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)],[128]) ).
thf(185,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(945,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
thf(930,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)],[178]) ).
thf(429,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
thf(1458,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)],[429]) ).
thf(356,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(1310,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
thf(533,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)],[4]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
thf(1164,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)],[291]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
thf(797,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)],[120]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
thf(1342,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)],[370]) ).
thf(97,axiom,
tc_IntDef_Oint @ ( c_0 @ c_Parity_Oeven ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
thf(747,plain,
tc_IntDef_Oint @ ( c_0 @ c_Parity_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
thf(913,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)],[169]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
thf(538,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)],[6]) ).
thf(376,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
thf(1354,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
thf(1095,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)],[258]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
thf(709,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)],[81]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(841,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)],[139]) ).
thf(509,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(1645,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)],[509]) ).
thf(378,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(1359,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
thf(565,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(55,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(651,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(324,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
thf(1243,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)],[324]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
thf(1127,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)],[274]) ).
thf(394,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(1391,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)],[394]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( c_0 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
thf(1576,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)],[481]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
thf(973,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)],[198]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
thf(1046,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)],[234]) ).
thf(490,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(1601,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(392,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
thf(1386,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)],[392]) ).
thf(344,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(1287,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
thf(570,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)],[17]) ).
thf(365,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(1330,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)],[365]) ).
thf(358,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
thf(1313,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)],[358]) ).
thf(427,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(1455,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
thf(934,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)],[180]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
thf(1055,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)],[238]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
thf(1409,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)],[403]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
thf(587,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)],[24]) ).
thf(362,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
thf(1323,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)],[362]) ).
thf(40,axiom,
( ( c_0 @ c_IntDef_Onat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
thf(619,plain,
( ( c_0 @ c_IntDef_Onat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(431,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
thf(1462,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(276,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
thf(1132,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)],[276]) ).
thf(468,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
thf(1545,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)],[468]) ).
thf(388,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
thf(1379,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)],[388]) ).
thf(455,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
thf(1514,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)],[455]) ).
thf(507,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(1641,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)],[507]) ).
thf(261,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(1100,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(969,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_div ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
thf(606,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)],[34]) ).
thf(218,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(1013,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
thf(770,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)],[108]) ).
thf(406,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(1415,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
thf(924,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)],[175]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
thf(756,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)],[102]) ).
thf(424,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(1450,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(26,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
thf(591,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)],[26]) ).
thf(523,axiom,
! [A: $i] :
( ( ( A @ ( c_1 @ c_HOL_Oabs ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
thf(1682,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)],[523]) ).
thf(284,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
thf(1151,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)],[284]) ).
thf(521,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(1677,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)],[521]) ).
thf(299,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(1183,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(408,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
thf(1418,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)],[408]) ).
thf(42,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(623,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
thf(1334,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)],[367]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
thf(646,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)],[53]) ).
thf(390,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(1383,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
thf(1020,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)],[221]) ).
thf(293,axiom,
tc_nat @ class_Power_Orecpower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(1169,plain,
tc_nat @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(387,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
thf(1377,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(91,axiom,
( ( c_1 @ c_IntDef_Oint )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
thf(734,plain,
( ( c_1 @ c_IntDef_Oint )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(247,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1072,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(396,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
thf(1394,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)],[396]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(998,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(415,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(1433,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(400,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).
thf(1405,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)],[400]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
thf(1104,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)],[263]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( B @ ( c_0 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
thf(1564,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)],[476]) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
thf(1215,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)],[313]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
thf(634,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)],[48]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(877,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)],[154]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
thf(692,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)],[73]) ).
thf(270,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(1119,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(500,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
thf(1622,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)],[500]) ).
thf(371,axiom,
tc_nat @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(1345,plain,
tc_nat @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(205,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(988,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(511,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(1651,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)],[511]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
thf(678,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)],[67]) ).
thf(354,axiom,
tc_IntDef_Oint @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(1306,plain,
tc_IntDef_Oint @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(1153,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(810,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)],[126]) ).
thf(357,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(1311,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(243,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(1067,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
thf(714,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)],[83]) ).
thf(505,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(1636,plain,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( A = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
thf(1074,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)],[248]) ).
thf(492,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
thf(1604,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)],[492]) ).
thf(2,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(529,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(526,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(1691,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
thf(1438,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)],[418]) ).
thf(60,axiom,
tc_nat @ ( c_0 @ c_Parity_Oeven ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
thf(661,plain,
tc_nat @ ( c_0 @ c_Parity_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Ojoin ) ) )
= B )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
thf(546,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)],[8]) ).
thf(118,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Onat )
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
thf(793,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)],[118]) ).
thf(338,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
thf(1274,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)],[338]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Omeet ) ) )
= B )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
thf(910,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)],[168]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
thf(825,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)],[132]) ).
thf(232,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
thf(1042,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)],[232]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
thf(1255,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(296,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/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
thf(1174,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)],[296]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(561,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)],[14]) ).
thf(442,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(1487,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
thf(630,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)],[46]) ).
thf(116,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
thf(788,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)],[116]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( c_0 @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
thf(1238,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)],[322]) ).
thf(190,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_div ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
thf(957,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(316,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
thf(1223,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)],[316]) ).
thf(161,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(894,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
thf(916,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)],[171]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
thf(847,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)],[142]) ).
thf(381,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
thf(1365,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(43,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(625,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(428,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(1457,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
thf(830,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)],[134]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
thf(889,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)],[159]) ).
thf(250,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(1079,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
thf(1291,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)],[347]) ).
thf(480,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
thf(1573,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)],[480]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
thf(1106,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)],[264]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
thf(852,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)],[144]) ).
thf(472,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/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
thf(1555,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)],[472]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
thf(1296,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)],[349]) ).
thf(62,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
thf(665,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
thf(1210,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)],[311]) ).
thf(513,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
thf(1656,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)],[513]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
thf(1195,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)],[305]) ).
thf(402,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(1407,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(374,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/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
thf(1350,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)],[374]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
thf(1089,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)],[256]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
thf(874,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)],[153]) ).
thf(332,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
thf(1259,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)],[332]) ).
thf(186,axiom,
! [A: $i] :
( ( ( A @ c_IntDef_Onat @ c_IntDef_Oint )
= c_0 )
| ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
thf(948,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)],[186]) ).
thf(463,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(1534,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)],[463]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
thf(615,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)],[38]) ).
thf(364,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(1328,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)],[364]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
thf(1064,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)],[242]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
thf(1227,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)],[318]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
thf(725,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)],[88]) ).
thf(27,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
thf(593,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(151,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(869,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
thf(783,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)],[114]) ).
thf(397,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
thf(1397,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)],[397]) ).
thf(95,axiom,
( ( c_0 @ c_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
thf(742,plain,
( ( c_0 @ c_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(578,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)],[20]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
thf(980,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)],[201]) ).
thf(448,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).
thf(1498,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)],[448]) ).
thf(466,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
thf(1540,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)],[466]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
thf(1006,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)],[215]) ).
thf(477,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(1567,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_2) ).
thf(884,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)],[157]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(1160,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(379,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(1361,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(514,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
thf(1659,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)],[514]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
thf(554,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)],[11]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
thf(669,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)],[64]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
thf(1424,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)],[410]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
thf(642,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)],[51]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(637,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(422,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(1446,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)],[422]) ).
thf(286,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(1155,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
thf(1028,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)],[225]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
thf(1082,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)],[252]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
thf(901,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)],[165]) ).
thf(70,axiom,
! [A: $i] :
( ( A = c_0 )
| ( ( A @ c_IntDef_Oint )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
thf(686,plain,
! [A: $i] :
( ( A = c_0 )
| ( ( A @ c_IntDef_Oint )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(496,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(1612,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)],[496]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
thf(1039,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)],[231]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(837,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
thf(1114,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)],[268]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
thf(701,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)],[77]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(1249,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)],[327]) ).
thf(461,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(1530,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)],[461]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
thf(1266,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)],[335]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
thf(654,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)],[57]) ).
thf(517,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(1668,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)],[517]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
thf(1552,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)],[471]) ).
thf(303,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(1192,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).
thf(1002,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)],[213]) ).
thf(412,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
thf(1429,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)],[412]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
thf(779,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)],[112]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(1627,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)],[502]) ).
thf(334,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
thf(1263,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)],[334]) ).
thf(210,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(997,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(485,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
thf(1588,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)],[485]) ).
thf(260,axiom,
tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
thf(1099,plain,
tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(203,axiom,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_IntDef_Oint @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
thf(985,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_IntDef_Oint @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(425,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).
thf(1451,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)],[425]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
thf(738,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)],[93]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
thf(1060,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)],[240]) ).
thf(236,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).
thf(1050,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(489,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(1599,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)],[489]) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
thf(1246,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)],[326]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(605,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)],[33]) ).
thf(395,axiom,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(1393,plain,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(416,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
thf(1434,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
thf(1086,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)],[254]) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
thf(1241,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)],[323]) ).
thf(123,axiom,
( ( tc_IntDef_Oint @ ( c_0 @ c_IntDef_Oint @ c_uminus ) )
= ( c_0 @ c_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
thf(805,plain,
( ( tc_IntDef_Oint @ ( c_0 @ c_IntDef_Oint @ c_uminus ) )
= ( c_0 @ c_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(173,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
thf(921,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
thf(541,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(294,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
thf(1170,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)],[294]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
thf(1035,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)],[229]) ).
thf(301,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
thf(1187,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(1026,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)],[224]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
thf(926,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)],[176]) ).
thf(433,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
thf(1466,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)],[433]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
thf(558,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)],[13]) ).
thf(246,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(1071,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(188,axiom,
( c_1
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(953,plain,
( c_1
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(300,axiom,
( ( c_0 @ c_Suc )
= ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
thf(1185,plain,
( ( c_0 @ c_Suc )
= ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
thf(662,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)],[61]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(718,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)],[85]) ).
thf(340,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(1278,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)],[340]) ).
thf(328,axiom,
tc_IntDef_Oint @ class_Power_Orecpower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(1251,plain,
tc_IntDef_Oint @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(282,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
thf(1146,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)],[282]) ).
thf(522,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(1680,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)],[522]) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(1483,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)],[440]) ).
thf(351,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(1301,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(18,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_div ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
thf(573,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
thf(689,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)],[71]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
thf(1374,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)],[386]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
thf(601,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)],[31]) ).
thf(277,axiom,
! [A: $i] :
( ~ ( A @ ( c_1 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
thf(1135,plain,
! [A: $i] :
( ~ ( A @ ( c_1 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_times ) ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
thf(1648,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)],[510]) ).
thf(194,axiom,
! [A: $i] :
( ~ ( A @ ( c_0 @ ( c_1 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
thf(965,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)],[194]) ).
thf(99,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(750,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ c_IntDef_Onat )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
thf(584,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)],[23]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
thf(819,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)],[130]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
thf(694,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)],[74]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= ( tc_nat @ ( B @ ( c_0 @ c_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(1615,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)],[497]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
thf(772,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)],[109]) ).
thf(499,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(1620,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)],[499]) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
thf(1388,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)],[393]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
thf(711,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)],[82]) ).
thf(399,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
thf(1403,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(457,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(1520,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)],[457]) ).
thf(443,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
thf(1488,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)],[443]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
thf(904,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)],[166]) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
thf(975,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)],[199]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
thf(843,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)],[140]) ).
thf(273,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
thf(1125,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)],[273]) ).
thf(450,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(1503,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
thf(936,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)],[181]) ).
thf(384,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(1371,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
thf(611,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)],[36]) ).
thf(239,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
thf(1058,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)],[239]) ).
thf(366,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
thf(1332,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)],[366]) ).
thf(432,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(1464,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(506,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
thf(1638,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)],[506]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
thf(1356,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)],[377]) ).
thf(520,axiom,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
thf(1675,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)],[520]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
thf(672,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)],[65]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
thf(764,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)],[106]) ).
thf(164,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(900,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( c_0 @ c_Nat_Opower ) ) )
= c_0 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
thf(681,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)],[68]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_0) ).
thf(1282,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)],[342]) ).
thf(269,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(1117,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(459,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
thf(1524,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)],[459]) ).
thf(281,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
thf(1144,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)],[281]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
thf(880,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)],[155]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_0) ).
thf(1122,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)],[272]) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
thf(1307,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)],[355]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
thf(863,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)],[148]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(1048,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ( c_1 @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
thf(736,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)],[92]) ).
thf(206,axiom,
~ ( tc_IntDef_Oint @ ( c_1 @ c_Parity_Oeven ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
thf(990,plain,
~ ( tc_IntDef_Oint @ ( c_1 @ c_Parity_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(209,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(996,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
thf(1492,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)],[445]) ).
thf(491,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
thf(1603,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)],[491]) ).
thf(479,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
thf(1571,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)],[479]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(599,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(435,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
thf(1471,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)],[435]) ).
thf(251,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
thf(1080,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(103,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_IntDef_Onat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
thf(758,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)],[103]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(816,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)],[129]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(609,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(1630,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)],[503]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
thf(594,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)],[28]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
thf(1162,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)],[290]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
thf(621,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)],[41]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
thf(895,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)],[162]) ).
thf(283,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(1149,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)],[283]) ).
thf(430,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(1460,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)],[430]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
thf(943,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)],[184]) ).
thf(389,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(1381,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)],[389]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ ( c_1 @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
thf(932,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)],[179]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(858,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)],[146]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(1557,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)],[473]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
thf(552,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)],[10]) ).
thf(44,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(626,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(170,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_IntDef_Oneg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
thf(915,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)],[170]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
thf(1112,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)],[267]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( c_1 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
thf(1688,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)],[525]) ).
thf(306,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(1198,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(487,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
thf(1594,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)],[487]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
thf(959,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)],[191]) ).
thf(150,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(868,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(508,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(1643,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
thf(1015,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)],[219]) ).
thf(204,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(986,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(563,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)],[15]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
thf(1000,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)],[212]) ).
thf(438,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_2) ).
thf(1477,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)],[438]) ).
thf(447,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(1496,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
thf(922,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)],[174]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
thf(658,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)],[59]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
thf(1213,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)],[312]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
thf(827,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)],[133]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(1044,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(325,axiom,
tc_nat @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(1245,plain,
tc_nat @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
= c_0 )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(675,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)],[66]) ).
thf(515,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(1662,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)],[515]) ).
thf(292,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(1166,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
thf(531,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)],[3]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ c_Suc @ c_IntDef_Oint )
= ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_1 @ c_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
thf(795,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)],[119]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
thf(648,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)],[54]) ).
thf(39,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
thf(617,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(220,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(1018,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
thf(754,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)],[101]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
thf(1181,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)],[298]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
thf(1203,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)],[308]) ).
thf(310,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
thf(1208,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)],[310]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
thf(589,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)],[25]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
thf(812,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)],[127]) ).
thf(453,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
thf(1509,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)],[453]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
thf(939,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)],[182]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).
thf(1340,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)],[369]) ).
thf(469,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(1547,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)],[469]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
thf(640,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)],[50]) ).
thf(223,axiom,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
thf(1025,plain,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(79,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
thf(705,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(158,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(887,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)],[158]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
thf(971,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)],[197]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ( B = c_1 )
| ( ( c_0 @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
thf(1252,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)],[329]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
thf(1230,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)],[319]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( A @ ( c_0 @ ( c_1 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
thf(580,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)],[21]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
thf(855,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)],[145]) ).
thf(317,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
thf(1225,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(398,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
thf(1400,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)],[398]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
thf(707,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)],[80]) ).
thf(414,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(1432,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ c_IntDef_Oint @ c_IntDef_Onat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
thf(791,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ c_IntDef_Onat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(360,axiom,
! [A: $i] :
( ( c_0 != c_1 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).
thf(1317,plain,
! [A: $i] :
( ( c_0 != c_1 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(482,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
thf(1579,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)],[482]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
thf(907,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)],[167]) ).
thf(465,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(1538,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
thf(951,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)],[187]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
thf(1285,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)],[343]) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
thf(1218,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)],[314]) ).
thf(96,axiom,
! [A: $i] :
( ( ( A @ c_IntDef_Onat @ c_IntDef_Oint )
= A )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
thf(744,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)],[96]) ).
thf(467,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(1543,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)],[467]) ).
thf(331,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(1257,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
thf(703,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)],[78]) ).
thf(464,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(1536,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(37,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(613,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
thf(1221,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)],[315]) ).
thf(375,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(1353,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(411,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
thf(1427,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)],[411]) ).
thf(518,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).
thf(1670,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)],[518]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
thf(1008,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)],[216]) ).
thf(385,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(1372,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
thf(1272,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)],[337]) ).
thf(498,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(1617,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)],[498]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
thf(656,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)],[58]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(1023,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(441,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(1485,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_1 @ ( B @ c_Nat_Opower ) ) )
= B )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
thf(1052,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)],[237]) ).
thf(484,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
thf(1585,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)],[484]) ).
thf(257,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(1094,plain,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(200,axiom,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_IntDef_Oneg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
thf(978,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_IntDef_Oneg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(279,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(1140,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
thf(845,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)],[141]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
thf(1421,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)],[409]) ).
thf(253,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(1084,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
thf(556,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)],[12]) ).
thf(524,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
thf(1685,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)],[524]) ).
thf(287,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(1157,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(405,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
thf(1412,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)],[405]) ).
thf(456,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).
thf(1517,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)],[456]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
thf(891,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)],[160]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
thf(1010,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)],[217]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(1453,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)],[426]) ).
thf(265,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
thf(1108,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)],[265]) ).
thf(423,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(1448,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)],[423]) ).
thf(302,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
thf(1189,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(339,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
thf(1276,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)],[339]) ).
thf(363,axiom,
( ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) )
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
thf(1326,plain,
( ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) )
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(76,axiom,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
thf(699,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)],[76]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
thf(961,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)],[192]) ).
thf(193,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(963,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)],[193]) ).
thf(437,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
thf(1476,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)],[437]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_minus ) ) )
= ( tc_nat @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
thf(748,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)],[98]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
thf(1101,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)],[262]) ).
thf(56,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
thf(652,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(47,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(632,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(781,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(1062,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(452,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(1508,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(731,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)],[90]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
thf(786,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)],[115]) ).
thf(226,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(1030,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(419,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
thf(1440,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(304,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
thf(1193,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
thf(1077,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)],[249]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(684,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)],[69]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
thf(536,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)],[5]) ).
thf(63,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_HOL_Oabs ) )
= ( A @ c_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
thf(667,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)],[63]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
thf(1294,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)],[348]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
thf(549,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)],[9]) ).
thf(421,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
thf(1444,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)],[421]) ).
thf(420,axiom,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ c_IntDef_Onat @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
thf(1442,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)],[420]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
thf(716,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)],[84]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
thf(800,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)],[121]) ).
thf(373,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
thf(1348,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)],[373]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
thf(752,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)],[100]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= ( tc_nat @ ( c_0 @ ( B @ c_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(1512,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)],[454]) ).
thf(341,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(1280,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(501,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(1625,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(352,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
thf(1303,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)],[352]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
thf(603,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)],[32]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
thf(833,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)],[135]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
thf(967,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)],[195]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(1097,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)],[259]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(835,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)],[136]) ).
thf(460,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
thf(1527,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)],[460]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ( tc_List_Ochar @ ( B @ ( A @ c_List_Ochar_OChar ) @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
thf(1673,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)],[519]) ).
thf(149,axiom,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
thf(865,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(439,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
thf(1480,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)],[439]) ).
thf(417,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
thf(1436,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)],[417]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(918,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)],[172]) ).
thf(380,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/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
thf(1363,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)],[380]) ).
thf(446,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(1495,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
thf(807,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)],[124]) ).
thf(475,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
thf(1561,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)],[475]) ).
thf(436,axiom,
! [A: $i] :
( ( c_1 != c_0 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__neq__zero_0) ).
thf(1473,plain,
! [A: $i] :
( ( c_1 != c_0 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
thf(696,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)],[75]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
thf(720,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)],[86]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
thf(955,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)],[189]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
thf(928,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)],[177]) ).
thf(295,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(1172,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(163,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(897,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
thf(767,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)],[107]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
thf(1033,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)],[228]) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
thf(1288,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)],[345]) ).
thf(372,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
thf(1346,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)],[372]) ).
thf(495,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(1610,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)],[495]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
thf(839,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)],[138]) ).
thf(321,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(1236,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)],[321]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
thf(1129,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)],[275]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
thf(1261,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)],[333]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
thf(575,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)],[19]) ).
thf(391,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(1384,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(483,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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(1582,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)],[483]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_g @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(528,plain,
! [A: $i] :
~ ( t_b @ ( t_b @ ( t_b @ ( A @ v_x @ v_g @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(644,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)],[52]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
thf(992,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)],[207]) ).
thf(87,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(723,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(131,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).
thf(822,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
thf(850,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)],[143]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(1299,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(72,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(691,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(451,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(1505,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(271,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
thf(1120,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
thf(728,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)],[89]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
thf(740,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)],[94]) ).
thf(462,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
thf(1532,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)],[462]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
thf(860,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)],[147]) ).
thf(488,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(1597,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)],[488]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
thf(982,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)],[202]) ).
thf(413,axiom,
tc_nat @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(1431,plain,
tc_nat @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
thf(1004,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)],[214]) ).
thf(493,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(1606,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)],[493]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
thf(803,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)],[122]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
thf(1320,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)],[361]) ).
thf(255,axiom,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(1088,plain,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).
thf(1069,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(156,axiom,
( ( c_1 @ c_IntDef_Onat )
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
thf(882,plain,
( ( c_1 @ c_IntDef_Onat )
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(407,axiom,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(1417,plain,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(512,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
thf(1653,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)],[512]) ).
thf(382,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
thf(1367,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)],[382]) ).
thf(444,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
thf(1490,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).
thf(1037,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(775,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)],[110]) ).
thf(1695,plain,
$false,
inference(e,[status(thm)],[1665,1337,1411,1469,1369,760,1633,1559,1315,941,1179,777,1549,1110,1501,809,628,1031,1200,1406,1290,1068,1522,994,1569,1205,1591,1692,1158,582,762,1142,1269,1305,597,1608,1137,1233,814,945,930,1458,1310,533,1164,797,1342,747,913,538,1354,1095,709,841,1645,1359,565,651,1243,1127,1391,1576,973,1046,1601,1386,1287,570,1330,1313,1455,934,1055,1409,587,1323,619,1462,1132,1545,1379,1514,1641,1100,969,606,1013,770,1415,924,756,1450,591,1682,1151,1677,1183,1418,623,1334,646,1383,1020,1169,1377,734,1072,1394,998,1433,1405,1104,1564,1215,634,877,692,1119,1622,1345,988,1651,678,1306,1153,810,1311,1067,714,1636,1074,1604,529,1691,1438,661,546,793,1274,910,825,1042,1255,1174,561,1487,630,788,1238,957,1223,894,916,847,1365,625,1457,830,889,1079,1291,1573,1106,852,1555,1296,665,1210,1656,1195,1407,1350,1089,874,1259,948,1534,615,1328,1064,1227,725,593,869,783,1397,742,578,980,1498,1540,1006,1567,884,1160,1361,1659,554,669,1424,642,637,1446,1155,1028,1082,901,686,1612,1039,837,1114,701,1249,1530,1266,654,1668,1552,1192,1002,1429,779,1627,1263,997,1588,1099,985,1451,738,1060,1050,1599,1246,605,1393,1434,1086,1241,805,921,541,1170,1035,1187,1026,926,1466,558,1071,953,1185,662,718,1278,1251,1146,1680,1483,1301,573,689,1374,601,1135,1648,965,750,584,819,694,1615,772,1620,1388,711,1403,1520,1488,904,975,843,1125,1503,936,1371,611,1058,1332,1464,1638,1356,1675,672,764,900,681,1282,1117,1524,1144,880,1122,1307,863,1048,736,990,996,1492,1603,1571,599,1471,1080,758,816,609,1630,594,1162,621,895,1149,1460,943,1381,932,858,1557,552,626,915,1112,1688,1198,1594,959,868,1643,1015,986,563,1000,1477,1496,922,658,1213,827,1044,1245,675,1662,1166,531,795,648,617,1018,754,1181,1203,1208,589,812,1509,939,1340,1547,640,1025,705,887,971,1252,1230,580,855,1225,1400,707,1432,791,1317,1579,907,1538,951,1285,1218,744,1543,1257,703,1536,613,1221,1353,1427,1670,1008,1372,1272,1617,656,1023,1485,1052,1585,1094,978,1140,845,1421,1084,556,1685,1157,1412,1517,891,1010,1453,1108,1448,1189,1276,1326,699,961,963,1476,748,1101,652,632,781,1062,1508,731,786,1030,1440,1193,1077,684,536,667,1294,549,1444,1442,716,800,1348,752,1512,1280,1625,1303,603,833,967,1097,835,1527,1673,865,1480,1436,918,1363,1495,807,1561,1473,696,720,955,928,1172,897,767,1033,1288,1346,1610,839,1236,1129,1261,575,1384,1582,528,644,992,723,822,850,1299,691,871,1505,1120,728,740,1532,860,1597,982,1431,1004,1606,803,1320,1088,1069,882,1417,1653,1367,1490,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA045-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 22:10:02 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.75/1.51 % [INFO] Parsing done (536ms).
% 2.75/1.52 % [INFO] Running in sequential loop mode.
% 3.31/1.89 % [INFO] eprover registered as external prover.
% 3.46/1.90 % [INFO] Scanning for conjecture ...
% 4.28/2.20 % [INFO] Found a conjecture (or negated_conjecture) and 2782 axioms. Running axiom selection ...
% 5.76/2.54 % [INFO] Axiom selection finished. Selected 525 axioms (removed 2257 axioms).
% 6.37/2.74 % [INFO] Problem is propositional (TPTP CNF).
% 6.37/2.76 % [INFO] Type checking passed.
% 6.37/2.77 % [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 ...
% 14.49/4.73 % External prover 'e' found a proof!
% 14.49/4.73 % [INFO] Killing All external provers ...
% 14.49/4.73 % Time passed: 4193ms (effective reasoning time: 3197ms)
% 14.49/4.73 % Axioms used in derivation (525): clsarity_IntDef__Oint_34, cls_IntDef_Ozero__less__int__conv_0, cls_Parity_Opower__less__zero__eq__number__of_0, cls_Nat_Onot__gr0_0, cls_IntDiv_Ozdiv__zadd__self1_0, cls_OrderedGroup_Ojoin__0__eq__0_1, cls_Divides_Odiv__mult__self1_0, cls_Parity_Opower__le__zero__eq__number__of_1, cls_Power_Opower__0__Suc_0, cls_Nat_Oone__eq__mult__iff_0, cls_NatArith_Oadd__diff__assoc2_0, cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0, cls_Power_Onat__zero__less__power__iff_2, cls_Nat_Onot__less0_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_IntDef_Ozless__nat__conj_1, cls_Parity_Oeven__nat__power_2, cls_IntDef_Ozless__int_0, cls_IntDef_Oint__eq__0__conv_1, cls_Parity_Oeven__sum_2, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Nat_Onat__add__left__cancel__less_1, cls_NatBin_Opower__nat__number__of__number__of_1, cls_Parity_Opower__eq__0__iff__number__of_2, cls_Divides_Omod__eq__0D__dest_0, cls_IntDiv_Ozmod__self_0, cls_Nat_Onat__add__right__cancel_0, cls_Parity_Ozero__less__power__eq__number__of_4, cls_IntDef_Oof__int__0__le__iff_0, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oordered__idom_12, clsrel_Ring__and__Field_Ofield_8, cls_IntDiv_Ozmod__zmult__self1_0, cls_Parity_Oeven__difference_2, cls_IntDef_Oof__int__0__less__iff_0, cls_Nat_Oop_A_K_Omult__Suc_0, clsarity_IntDef__Oint_52, clsarity_IntDef__Oint_24, cls_Parity_Oeven__nat__product_2, cls_IntDiv_Ozdiv__1_0, cls_IntDef_Oint__nat__eq_0, cls_Nat_Omult__le__cancel1_1, cls_Parity_Oeven__nat__product_1, cls_Nat_Oless__one_1, clsrel_Power_Orecpower_21, clsrel_Ring__and__Field_Oordered__semidom_28, cls_Nat_Odiff__is__0__eq_0, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_OrderedGroup_Opprt__eq__id_0, cls_Parity_Oeven__nat__sum_1, cls_Nat_OSuc__Suc__eq_0, clsarity_nat_40, cls_Nat_Oop_A_K_Omult__0_0, cls_Power_Ozero__less__power__abs__iff_2, cls_IntDiv_Ozdiv__zminus__zminus_0, clsrel_Ring__and__Field_Ofield_32, clsrel_Ring__and__Field_Ofield_5, cls_Parity_Ozero__less__power__eq__number__of_1, cls_IntDef_Oint__Suc_0, cls_IntDiv_Ozero__less__zpower__abs__iff_2, cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_IntDef_Onegative__eq__positive_0, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, cls_IntDiv_ODIVISION__BY__ZERO_0, cls_Nat_Odiff__0__eq__0_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_IntDef_Oneg__zminus__int_0, cls_Divides_Odiv__less_0, cls_Divides_Odiv__1_0, cls_NatBin_Oint__nat__number__of_1, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__0__eq_0, clsarity_IntDef__Oint_56, cls_IntDef_Oint__less__0__conv_0, cls_OrderedGroup_Onprt__mono_0, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_NatBin_Oeq__0__number__of_1, cls_OrderedGroup_Oneg__meet__eq__join_0, cls_Ring__and__Field_Omult__cancel__left1_2, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Onat__le__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_Nat_Ozero__less__diff_1, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_IntDiv_Ozmod__zmult__self2_0, cls_IntDef_Ozero__less__int__conv_1, cls_NatBin_OSuc__nat__number__of_0, cls_Numeral_Obin__rel__simps__9_0, cls_Power_Opower_Osimps__2_0, cls_Divides_Omod__add__self1_0, cls_Parity_Opower__0__left__number__of_1, cls_Power_Opower__one__right_0, cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0, cls_IntDef_Oof__int__less__iff_0, clsarity_nat_29, cls_Nat_Omult__less__cancel2_1, cls_NatArith_Odiff__diff__right_0, cls_Divides_Odiv__mult__self__is__m_0, cls_IntDiv_Omod__div__trivial_0, cls_Power_Opower__eq__0__iff_2, clsarity_IntDef__Oint_0, cls_Ring__and__Field_Ofield__mult__cancel__left_1, cls_Parity_Oeven__power_2, cls_Nat_Omult__0__right_0, cls_LOrder_Ojoin__idempotent_0, cls_Nat_Onat__add__left__cancel__le_0, cls_Ring__and__Field_Omult__cancel__right1_2, cls_Divides_Odiv__less__dividend_0, cls_List_Ochar_Oinject_0, cls_OrderedGroup_Omeet__0__eq__0_0, cls_NatBin_Odiv__nat__number__of_0, cls_Nat_Omult__less__cancel1_1, cls_Nat_Omult__eq__1__iff_0, cls_IntDef_Onot__neg__int_0, cls_Nat_Oadd__gr__0_2, clsrel_OrderedGroup_Olordered__ab__group__abs_0, cls_Nat_Onat__add__left__cancel__less_0, cls_NatBin_Odiv__nat__number__of_1, clsrel_Ring__and__Field_Ofield_17, cls_Power_Opower__strict__increasing__iff_0, cls_Power_Ozero__le__power__abs_0, cls_OrderedGroup_Oabs__eq__0_0, clsarity_nat_36, cls_IntDef_Ozero__less__nat__eq_1, cls_IntArith_Oint__eq__iff__number__of_1, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, cls_Power_Opower__increasing__iff_1, cls_Nat_Odiff__Suc__Suc_0, clsrel_Ring__and__Field_Oordered__semidom_35, cls_Nat_Omult__eq__1__iff_2, cls_Nat_Omult__le__cancel1_0, cls_IntDef_Oof__int__le__0__iff_1, cls_Parity_Oeven__neg_0, cls_Nat_Oless__one_0, cls_IntDiv_Omod__mod__trivial_0, cls_IntDef_Oint__nat__eq_1, clsarity_IntDef__Oint_48, clsrel_OrderedGroup_Olordered__ab__group_6, cls_Nat_Ole__add__diff__inverse2_0, cls_Parity_Ozero__less__power__nat__eq__number__of_1, clsarity_IntDef__Oint_58, cls_Divides_Omod__le__divisor_0, clsrel_Ring__and__Field_Oordered__idom_38, cls_Nat_Omult__less__cancel2_0, cls_IntDiv_Opower_Osimps__2_0, cls_Parity_Oeven__nat__power_0, cls_Parity_Ozero__less__power__nat__eq__number__of_0, clsrel_Ring__and__Field_Oordered__idom_51, cls_Power_Onat__one__le__power_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_Parity_Ozero__le__power__eq__number__of_1, cls_IntDef_Onegative__eq__positive_2, cls_Parity_Opower__le__zero__eq__number__of_5, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Ring__and__Field_Oordered__idom_52, cls_Parity_Oeven__sum_0, cls_Parity_Oeven__product_0, cls_IntDef_Oof__int__less__iff_1, clsrel_Ring__and__Field_Oordered__idom_36, cls_Divides_Omod__mult__self1_0, cls_Power_Ozero__less__power__abs__iff_0, cls_OrderedGroup_Ozero__le__pprt_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, cls_Nat_Oadd__is__0_1, cls_Parity_Opower__eq__0__iff__number__of_1, cls_Parity_Oeven__nat__power_1, cls_OrderedGroup_Ojoin__0__eq__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_Power_Orecpower__class_Oaxioms__1_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0, cls_Ring__and__Field_Onot__one__le__zero_0, cls_Nat_Omult__le__cancel2_2, clsrel_Ring__and__Field_Oordered__idom_47, cls_IntDef_Oof__int__0__le__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_36, cls_Parity_Oeven__difference_1, cls_Parity_Opower__le__zero__eq__number__of_0, clsrel_OrderedGroup_Olordered__ab__group_17, cls_Power_Ozero__less__power__abs__iff_1, cls_Nat_Omult__cancel1_1, cls_OrderedGroup_Onprt__le__zero_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, cls_Nat_Onat__0__less__mult__iff_0, cls_Divides_Onat__mod__div__trivial_0, cls_IntDiv_Ozero__less__zpower__abs__iff_1, cls_IntDef_Oof__int__eq__iff_0, clsrel_Ring__and__Field_Oordered__idom_18, clsrel_Ring__and__Field_Oordered__ring__strict_16, cls_Ring__and__Field_Omult__cancel__right1_1, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_Divides_Odiv__mult__self1__is__m_0, cls_NatBin_Omod__nat__number__of_1, cls_IntDef_Oof__int__0__eq__iff_0, cls_Divides_Odiv__mult__mult2_0, cls_Nat_Ole__0__eq_0, cls_Power_Opower__inject__exp_0, cls_NatArith_Odiff__less_0, cls_Divides_ODIVISION__BY__ZERO__DIV_0, cls_Nat_Ozero__less__diff_0, cls_Parity_Oeven__sum_3, cls_Divides_Omod__add__self2_0, cls_Parity_Oeven__nat__sum_0, cls_Power_Opower_Osimps__1_0, cls_Power_Opower__eq__0__iff_0, cls_Nat_OSuc__le__mono_0, cls_Ring__and__Field_Omult__cancel__left1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_6, cls_IntDef_Oabs__int__eq_0, cls_Parity_Opower__le__zero__eq__number__of_4, cls_Parity_Ozero__less__power__eq__number__of_3, cls_List_Odrop__0_0, cls_Ring__and__Field_Omult__eq__0__iff_0, cls_IntDiv_Ozdiv__zero_0, cls_IntDiv_Opos__mod__sign_0, cls_Nat_Oone__le__mult__iff_1, clsrel_Ring__and__Field_Oordered__idom_11, cls_Nat_OSuc__less__eq_1, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsarity_nat_37, cls_Parity_Oeven__nat__zero_0, cls_IntDef_Oint__int__eq_0, clsrel_LOrder_Olorder_0, cls_Nat_Omult__less__cancel1_0, cls_Ring__and__Field_Ozero__le__one_0, cls_Divides_Omod__mult__self1__is__0_0, cls_Parity_Opower__0__left__number__of_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, cls_Divides_Omod__less__divisor_0, cls_Nat_Omult__cancel2_0, clsarity_IntDef__Oint_37, clsrel_Ring__and__Field_Oordered__semidom_12, cls_Ring__and__Field_Omult__cancel__left2_0, cls_Parity_Oeven__power_1, clsarity_nat_6, cls_Power_Opower__strict__increasing__iff_1, cls_IntDef_Ozless__nat__conj_2, clsarity_nat_43, cls_NatBin_Oint__nat__number__of_0, cls_IntDef_Onegative__eq__positive_1, cls_NatBin_Oeq__nat__number__of_10, cls_Divides_Omod__1_0, cls_Nat_Omult__cancel2_1, cls_IntArith_Oone__less__nat__eq_1, clsrel_OrderedGroup_Olordered__ab__group__abs_16, cls_IntArith_Oint__eq__iff__number__of_0, cls_Nat_Onat__0__less__mult__iff_1, clsrel_Power_Orecpower_3, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_Ring__and__Field_Oordered__idom_46, clsarity_nat_45, clsrel_OrderedGroup_Olordered__ab__group__meet_15, cls_IntDiv_Ozmod__zero_0, cls_Nat_OSuc__diff__diff_0, cls_OrderedGroup_Opprt__0_0, cls_NatBin_Omod__nat__number__of_2, clsarity_IntDef__Oint_18, clsarity_nat_34, cls_Parity_Ozero__less__power__nat__eq__number__of_2, cls_Nat_OSuc__le__mono_1, clsrel_Ring__and__Field_Oordered__ring__strict_35, clsarity_nat_17, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1, cls_NatBin_Omult__nat__number__of_0, cls_IntDef_Oof__int__less__0__iff_0, cls_OrderedGroup_Opprt__eq__0_0, cls_IntDiv_Ozdiv__zmult__self1_0, cls_NatBin_Onat__number__of_0, clsrel_Ring__and__Field_Oordered__semidom_36, cls_Divides_Omod__mult__self2_0, cls_OrderedGroup_Oabs__of__nonpos_0, cls_NatArith_Odiff__Suc__diff__eq2_0, cls_IntArith_Ozle__add1__eq__le_1, cls_Parity_Oeven__nat__Suc_1, cls_NatBin_Oadd__nat__number__of_1, cls_OrderedGroup_Opprt__mono_0, cls_IntDef_Onat__int_0, cls_Ring__and__Field_Oright__inverse_0, clsarity_IntDef__Oint_54, cls_IntArith_Ozabs__less__one__iff_0, cls_Nat_Odiff__is__0__eq_H_0, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_Ring__and__Field_Oordered__idom_35, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, cls_Nat_Oadd__gr__0_0, clsrel_OrderedGroup_Olordered__ab__group__join_16, cls_NatBin_Oone__mod__nat__number__of_0, cls_OrderedGroup_Oabs__minus__cancel_0, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_Parity_Opower__le__zero__eq__number__of_3, cls_Nat_Oless__Suc0_0, cls_IntDef_Oint__1_0, cls_IntDef_Onot__zle__0__negative_0, cls_OrderedGroup_Ozero__less__abs__iff_1, cls_Nat_Oadd__is__0_2, cls_Nat_Oop_A_N_Odiff__0_0, cls_Parity_Opower__less__zero__eq__number__of_2, cls_OrderedGroup_Onprt__eq__0_0, cls_Parity_Oeven__difference_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_IntArith_Ozle__diff1__eq_0, cls_Nat_Onot__add__less1_0, cls_Parity_Oodd__one_0, clsrel_Ring__and__Field_Oordered__ring__strict_24, cls_NatArith_Odiff__diff__cancel_0, cls_OrderedGroup_Oabs__eq__0_1, cls_Ring__and__Field_Omult__cancel__left1_0, cls_Ring__and__Field_Onot__one__less__zero_0, cls_NatBin_Omod__nat__number__of_0, cls_Parity_Oeven__nat__sum_2, clsrel_OrderedGroup_Olordered__ab__group_15, clsrel_Ring__and__Field_Oordered__idom_41, cls_IntDef_Onot__int__zless__negative_0, clsarity_IntDef__Oint_32, clsrel_Ring__and__Field_Oordered__ring__strict_28, cls_Parity_Oeven__product_1, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_Nat_Omult__cancel1_0, cls_Parity_Ozero__less__power__eq__number__of_2, cls_IntDiv_Ozmod__zadd__self2_0, cls_OrderedGroup_Oabs__le__zero__iff_0, cls_Parity_Oeven__power_0, clsarity_IntDef__Oint_22, cls_Nat_Omult__le__cancel2_1, clsrel_Ring__and__Field_Oordered__ring__strict_3, cls_Nat_Oone__eq__mult__iff_2, cls_Nat_Odiff__Suc__less_0, cls_Ring__and__Field_Omult__zero__right_0, clsarity_nat_5, cls_Ring__and__Field_Oone__neq__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_2, cls_Nat_OOne__nat__def_0, cls_IntDiv_Oneg__mod__bound_0, cls_Nat_Oadd__0__right_0, cls_Nat_Ole__add__diff__inverse_0, cls_Power_Onat__zero__less__power__iff_1, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_IntDiv_Oneg__mod__sign_0, clsrel_Ring__and__Field_Oordered__idom_8, cls_Nat_Onot__gr0_1, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, cls_Nat_Onot__add__less2_0, cls_Nat_Oadd__Suc__right_0, cls_IntDiv_Ozero__less__zpower__abs__iff_0, clsrel_Ring__and__Field_Oordered__semidom_26, cls_IntDef_Ozless__int_1, cls_IntDiv_Ozmod__eq__0D__dest_0, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, cls_Ring__and__Field_Oabs__one_0, clsarity_nat_9, cls_Ring__and__Field_Omult__cancel__right2_0, cls_Ring__and__Field_Ofield__mult__cancel__right_0, cls_IntDef_Oof__int__eq__0__iff_0, cls_NatArith_Odiff__Suc__diff__eq1_0, cls_Nat_Oone__le__mult__iff_0, cls_Parity_Oeven__sum_1, cls_Ring__and__Field_Ofield__mult__cancel__right_1, cls_Nat_Odiff__diff__left_0, cls_Parity_Ozero__less__power__eq__number__of_5, clsrel_Ring__and__Field_Oordered__semidom_5, clsarity_IntDef__Oint_33, cls_Parity_Opower__less__zero__eq__number__of_1, cls_Parity_Opower__le__zero__eq__number__of_2, cls_Divides_Omod__less_0, cls_Parity_Oeven__zero_0, cls_IntArith_Ozabs__less__one__iff_1, cls_IntDef_Ozero__zle__int_0, cls_NatArith_Oadd__diff__assoc_0, clsrel_Ring__and__Field_Oordered__semidom_6, cls_Parity_Ozero__le__power__eq__number__of_0, clsrel_Ring__and__Field_Ofield_11, clsrel_Ring__and__Field_Oordered__ring__strict_34, cls_Divides_Omod__self_0, cls_IntArith_Onat__1_0, cls_IntDef_Oof__int__le__iff_1, cls_Divides_Odiv__0_0, cls_Divides_Odiv__mult__mult1_0, cls_Nat_OSuc__not__Zero_0, cls_OrderedGroup_Oabs__0__eq_1, cls_Nat_Omult__less__cancel1_2, cls_IntDef_Oof__int__0__less__iff_1, cls_OrderedGroup_Onprt__0_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, cls_Power_Opower__eq__0__iff_1, cls_IntDiv_Ozdiv__zadd__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_20, clsrel_Power_Orecpower_9, clsrel_Ring__and__Field_Oordered__ring__strict_18, clsrel_OrderedGroup_Olordered__ab__group_2, cls_IntDef_Oof__int__less__0__iff_1, cls_IntDef_Ozle__int_1, cls_Divides_Odiv__mult__self2_0, clsrel_Ring__and__Field_Oordered__ring__strict_29, cls_IntDef_Oof__int__le__0__iff_0, cls_Nat_Oless__Suc0_1, cls_IntDef_Oint__eq__0__conv_0, cls_Divides_ODIVISION__BY__ZERO__MOD_0, cls_IntDiv_Ozero__le__zpower__abs_0, cls_IntDiv_Ozdiv__self_0, clsrel_Ring__and__Field_Oordered__semidom_29, cls_Ring__and__Field_Omult__zero__left_0, clsrel_OrderedGroup_Olordered__ab__group__abs_7, cls_IntDiv_Ozdiv__zmult__self2_0, cls_Parity_Oeven__nat__Suc_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0, cls_Nat_Onat__add__left__cancel_0, cls_IntDef_Oof__int__0__eq__iff_1, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, cls_IntDef_Onegative__zle_0, clsarity_nat_13, clsrel_Ring__and__Field_Oordered__idom_34, cls_Divides_Onat__mod__mod__trivial_0, cls_Ring__and__Field_Omult__cancel__right1_0, cls_Nat_Oone__le__mult__iff_2, cls_Parity_Ozero__less__power__eq__number__of_0, cls_Power_Opower__one_0, cls_Parity_Oeven__nat__product_0, cls_IntArith_Ozle__add1__eq__le_0, clsarity_nat_24, cls_List_Olexn_Osimps__1_0, clsrel_OrderedGroup_Ocomm__monoid__mult_1, cls_NatBin_Oone__mod__nat__number__of_1, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsarity_IntDef__Oint_51, cls_IntArith_Ozle__diff1__eq_1, cls_Nat_Ole0_0, cls_Nat_OSuc__less__eq_0, cls_Parity_Oeven__nat__sum_3, cls_Parity_Opower__eq__0__iff__number__of_0, clsarity_nat_4, cls_IntArith_Oone__less__nat__eq_0, cls_NatBin_Oone__div__nat__number__of_0, cls_Nat_Oop_A_L_Oadd__0_0, clsarity_IntDef__Oint_23, cls_Parity_Oeven__difference_3, cls_Nat_Oadd__gr__0_1, clsarity_IntDef__Oint_63, cls_IntDiv_Opower_Osimps__1_0, cls_IntDef_Oint__0__neq__1_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0, cls_NatBin_Oadd__nat__number__of_0, cls_IntDef_Ozless__nat__conj_0, clsrel_Ring__and__Field_Oordered__semidom_30, cls_IntDiv_Opos__mod__bound_0, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_IntDef_Ozero__less__nat__eq_0, clsarity_IntDef__Oint_50, cls_List_Ochar_Oinject_1, cls_OrderedGroup_Oabs__of__nonneg_0, cls_Nat_Omult__le__cancel1_2, cls_Power_Opower__increasing__iff_0, cls_Divides_Odiv__le__dividend_0, cls_Parity_Oeven__product_2, clsrel_Power_Orecpower_16, cls_Nat_Oop_A_L_Oadd__Suc_0, clsarity_IntDef__Oint_55, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, cls_Nat_Ole__0__eq_1, cls_IntArith_Oint__eq__iff__number__of_2, clsrel_Ring__and__Field_Ofield_18, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Nat_Omult__le__cancel2_0, clsrel_OrderedGroup_Olordered__ab__group__meet_2, cls_IntDiv_Ozmod__zminus__zminus_0, cls_Nat_OZero__not__Suc_0, cls_Divides_Omod__mult__self__is__0_0, clsrel_Ring__and__Field_Oordered__ring__strict_2, cls_Nat_OlessI_0, cls_IntDef_Oof__int__eq__0__iff_1, cls_OrderedGroup_Oabs__idempotent_0, cls_Nat_Omult__less__cancel2_2, cls_Divides_Odiv__self_0, cls_IntDef_Onat__zero_0, cls_Divides_Omod__0_0, cls_OrderedGroup_Oabs__le__zero__iff_1, cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0, cls_Nat_OSuc__pred_0, cls_Nat_Omult__eq__1__iff_1, cls_NatBin_Oeq__number__of__0_1, cls_Nat_Omult__Suc__right_0, cls_Ring__and__Field_Ofield__mult__cancel__left_0, cls_IntDef_Oint__le__0__conv_0, cls_Nat_Oone__eq__mult__iff_1, cls_List_Ochar_Osize_0, clsrel_Ring__and__Field_Ofield_12, cls_Parity_Opower__even__abs__number__of_0, cls_Parity_Oeven__neg_1, cls_IntDef_Onegative__zless_0, cls_OrderedGroup_Omeet__0__eq__0_1, cls_OrderedGroup_Oneg__join__eq__meet_0, cls_IntDiv_Ozmod__1_0, cls_IntDef_Onat__zminus__int_0, cls_List_Odrop__drop_0, cls_Nat_Omult__is__0_0, cls_IntDiv_Ozmod__zadd__self1_0, cls_Parity_Ozero__le__power__eq__number__of_2, cls_IntDef_Oint__le__0__conv_1, cls_Power_Onat__zero__less__power__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_18, cls_IntDef_Ozle__int_0, clsarity_IntDef__Oint_9
% 14.49/4.73 % No. of inferences in proof: 1055
% 14.49/4.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4193 ms resp. 3197 ms w/o parsing
% 15.45/4.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.45/4.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------