%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA044-1 : 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 : n017.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 06:50:22 AM UTC 2026
% Result : Unsatisfiable 46.38s 11.40s
% Output : Refutation 53.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 784
% Syntax : Number of formulae : 1569 ( 401 unt; 0 typ; 0 def)
% Number of atoms : 3237 ( 728 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 13152 (1606 ~;1668 |; 0 &;9878 @)
% ( 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 : 95 ( 93 usr; 15 con; 0-3 aty)
% Number of variables : 2716 ( 0 ^;2716 !; 0 ?;2716 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(v_l_decl,type,
v_l: $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(v_h_decl,type,
v_h: $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_xa_decl,type,
v_xa: $i ).
thf(v_A_decl,type,
v_A: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(t_d_decl,type,
t_d: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_k_decl,type,
v_k: $i > $i > $i ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $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(c_UNIV_decl,type,
c_UNIV: $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(tc_nat_decl,type,
tc_nat: $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(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_SetInterval_OlessThan_decl,type,
c_SetInterval_OlessThan: $i > $i > $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(c_div_decl,type,
c_div: $i > $i > $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $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_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $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(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1__cancel_decl,type,
class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).
thf(c_NatArith_Oof__nat_decl,type,
c_NatArith_Oof__nat: $i > $i > $i ).
thf(c_IntDef_Onat_decl,type,
c_IntDef_Onat: $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_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(c_IntDef_Oof__int_decl,type,
c_IntDef_Oof__int: $i > $i > $i ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_HOL_Otimes_decl,type,
class_HOL_Otimes: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(c_SetInterval_OgreaterThanLessThan_decl,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(class_LOrder_Olorder_decl,type,
class_LOrder_Olorder: $i > $o ).
thf(c_SetInterval_OatLeastAtMost_decl,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0__cancel_decl,type,
class_Ring__and__Field_Osemiring__0__cancel: $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_OrderedGroup_Olordered__ab__group__join_decl,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(c_SetInterval_OgreaterThanAtMost_decl,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $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_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_SetsAndFunctions_Oelt__set__times_decl,type,
c_SetsAndFunctions_Oelt__set__times: $i > $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_IntDef_OInts_decl,type,
c_IntDef_OInts: $i ).
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_SetInterval_OgreaterThan_decl,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_IntDef_ONats_decl,type,
c_IntDef_ONats: $i ).
thf(c_HOL_Oinverse_decl,type,
c_HOL_Oinverse: $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Oall__not__in__conv__1_decl,type,
c_Main_Oall__not__in__conv__1: $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_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Ochar_decl,type,
tc_List_Ochar: $i ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
thf(1879,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(609,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(2094,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)],[609]) ).
thf(727,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(2341,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ c_NatArith_Oof__nat ) )
= ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ c_NatArith_Oof__nat ) )
= ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(599,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(2072,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)],[599]) ).
thf(201,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(1237,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(57,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(909,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)],[57]) ).
thf(517,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(1899,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)],[517]) ).
thf(49,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(893,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)],[49]) ).
thf(235,axiom,
( ( c_1 @ c_IntDef_Onat )
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
thf(1315,plain,
( ( c_1 @ c_IntDef_Onat )
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(72,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(941,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)],[72]) ).
thf(723,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(2331,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)],[723]) ).
thf(542,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(1950,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
thf(2199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(408,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(1665,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(367,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
thf(1586,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(324,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(1501,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(772,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(2452,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)],[772]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(261,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(1369,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)],[261]) ).
thf(179,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(1190,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)],[179]) ).
thf(478,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(1818,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)],[478]) ).
thf(227,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(1295,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(701,axiom,
! [A: $i] :
( ( A @ ( c_IntDef_OInts @ ( c_0 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
thf(2280,plain,
! [A: $i] :
( ( A @ ( c_IntDef_OInts @ ( c_0 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(353,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(1554,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)],[353]) ).
thf(145,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(1110,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(418,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(1686,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)],[418]) ).
thf(688,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(2250,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)],[688]) ).
thf(736,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(2363,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)],[736]) ).
thf(165,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(1158,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)],[165]) ).
thf(622,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(2117,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(679,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(2231,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(595,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(2062,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)],[595]) ).
thf(385,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(1618,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)],[385]) ).
thf(95,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(994,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)],[95]) ).
thf(276,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(1401,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)],[276]) ).
thf(129,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(1073,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)],[129]) ).
thf(570,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
thf(2014,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
thf(1728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(420,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(1692,plain,
! [A: $i] :
( ~ ( A @ ( c_1 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(1305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(172,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(1173,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)],[172]) ).
thf(360,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(1569,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)],[360]) ).
thf(687,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(2248,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(40,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(873,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)],[40]) ).
thf(187,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(1205,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)],[187]) ).
thf(702,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(2282,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)],[702]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__times ) ) @ ( A @ ( B @ ( D @ c_SetsAndFunctions_Oelt__set__times ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono_0) ).
thf(1591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__times ) ) @ ( A @ ( B @ ( D @ c_SetsAndFunctions_Oelt__set__times ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(621,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(2114,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)],[621]) ).
thf(216,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
= ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
thf(1269,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
= ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(42,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(878,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)],[42]) ).
thf(742,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(2380,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)],[742]) ).
thf(552,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(1971,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(467,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
thf(1793,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(342,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(1533,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(379,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(1608,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(450,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(1756,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(581,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(2035,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(633,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(2141,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)],[633]) ).
thf(503,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
thf(1872,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(199,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(1233,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)],[199]) ).
thf(648,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
thf(2168,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(559,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(1988,plain,
( ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) )
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(248,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(1342,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)],[248]) ).
thf(544,axiom,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(1954,plain,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(636,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( E @ c_times ) ) @ ( A @ tc_set @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono2_0) ).
thf(2146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( E @ c_times ) ) @ ( A @ tc_set @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(66,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(930,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)],[66]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
thf(1497,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ c_uminus ) @ c_Nat_Opower ) ) )
= ( A @ ( B @ ( C @ c_Nat_Opower ) ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
thf(1705,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ c_uminus ) @ c_Nat_Opower ) ) )
= ( A @ ( B @ ( C @ c_Nat_Opower ) ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(465,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(1788,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)],[465]) ).
thf(288,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(1426,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)],[288]) ).
thf(168,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(1164,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(564,axiom,
! [A: $i] :
( ( ( A @ ( c_1 @ c_IntDef_Oof__int ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
thf(1999,plain,
! [A: $i] :
( ( ( A @ ( c_1 @ c_IntDef_Oof__int ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(16,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(814,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)],[16]) ).
thf(241,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(1327,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
thf(1095,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(485,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(672,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(2216,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)],[672]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(587,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(2046,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)],[587]) ).
thf(152,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_NatArith_Oof__nat ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
thf(1127,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_NatArith_Oof__nat ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
thf(1391,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(26,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(841,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(86,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(973,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)],[86]) ).
thf(382,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(1613,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)],[382]) ).
thf(568,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
thf(2010,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(255,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(1359,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)],[255]) ).
thf(375,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(1601,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(604,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(2082,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(311,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
thf(1475,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(259,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1366,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(511,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(1887,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(398,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(1645,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)],[398]) ).
thf(528,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(1921,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)],[528]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(519,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(1904,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)],[519]) ).
thf(334,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(1518,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)],[334]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ ( C @ c_minus ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ ( C @ c_minus ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(197,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(1228,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)],[197]) ).
thf(388,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
thf(1623,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(223,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(1287,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)],[223]) ).
thf(558,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(1985,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)],[558]) ).
thf(583,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(2039,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)],[583]) ).
thf(5,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(785,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(696,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(2269,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(239,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(1323,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)],[239]) ).
thf(60,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(917,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(11,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(802,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)],[11]) ).
thf(234,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(1313,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)],[234]) ).
thf(656,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(2185,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(484,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(1832,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)],[484]) ).
thf(561,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(1992,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)],[561]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( C @ c_minus ) ) @ c_NatArith_Oof__nat ) )
= ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( A @ ( C @ c_NatArith_Oof__nat ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( B @ ( C @ c_minus ) ) @ c_NatArith_Oof__nat ) )
= ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( A @ ( C @ c_NatArith_Oof__nat ) @ c_minus ) ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(733,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(2356,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)],[733]) ).
thf(121,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(1055,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)],[121]) ).
thf(280,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(1409,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)],[280]) ).
thf(452,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(1760,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)],[452]) ).
thf(406,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(1660,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)],[406]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
thf(1330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(497,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(1860,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)],[497]) ).
thf(778,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
thf(2466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(626,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
thf(2126,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(348,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(1545,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)],[348]) ).
thf(17,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(817,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(265,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(1379,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_div ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(161,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(1147,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)],[161]) ).
thf(588,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(2049,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(103,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(1013,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)],[103]) ).
thf(147,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(1115,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)],[147]) ).
thf(643,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
thf(2158,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(576,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(2024,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)],[576]) ).
thf(710,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(2301,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)],[710]) ).
thf(461,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(1778,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(753,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(2403,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)],[753]) ).
thf(134,axiom,
( ( c_1 @ c_IntDef_Oint )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
thf(1087,plain,
( ( c_1 @ c_IntDef_Oint )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(332,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_15) ).
thf(1514,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(84,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(969,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)],[84]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
thf(1347,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(256,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(1362,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(548,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(1963,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(567,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
thf(1489,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(577,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(2027,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(4,negated_conjecture,
( ( t_b @ ( v_xa @ ( v_x @ v_k ) @ v_h @ ( v_xa @ ( v_x @ v_l ) @ c_times ) ) )
!= ( t_b @ ( t_b @ ( v_xa @ ( v_x @ v_k ) @ v_h @ ( v_xa @ ( v_x @ v_l ) @ c_times ) ) @ c_HOL_Oabs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(789,plain,
( ( t_b @ ( v_xa @ ( v_x @ v_k ) @ v_h @ ( v_xa @ ( v_x @ v_l ) @ c_times ) ) )
!= ( t_b @ ( t_b @ ( v_xa @ ( v_x @ v_k ) @ v_h @ ( v_xa @ ( v_x @ v_l ) @ c_times ) ) @ c_HOL_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(263,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(1373,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)],[263]) ).
thf(523,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(1911,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(23,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(834,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)],[23]) ).
thf(555,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(1978,plain,
! [A: $i] :
( ( c_0 != c_1 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(70,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(937,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)],[70]) ).
thf(414,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(1677,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)],[414]) ).
thf(547,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(1960,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)],[547]) ).
thf(119,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(1051,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(653,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(2178,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)],[653]) ).
thf(674,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(2222,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)],[674]) ).
thf(540,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(1946,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(306,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(1465,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)],[306]) ).
thf(616,axiom,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(2105,plain,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(299,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
thf(1450,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(114,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(1040,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)],[114]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ c_uminus ) @ c_Nat_Opower ) ) )
= ( A @ ( A @ ( B @ ( C @ c_Nat_Opower ) ) @ c_uminus ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
thf(1632,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ c_uminus ) @ c_Nat_Opower ) ) )
= ( A @ ( A @ ( B @ ( C @ c_Nat_Opower ) ) @ c_uminus ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(284,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(1418,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(681,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
thf(2236,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(496,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
thf(1858,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(624,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
thf(2122,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(706,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(2291,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)],[706]) ).
thf(267,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(1383,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)],[267]) ).
thf(725,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(2335,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)],[725]) ).
thf(82,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(966,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(572,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(2017,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)],[572]) ).
thf(55,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(905,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)],[55]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
thf(981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(489,axiom,
tc_nat @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(1843,plain,
tc_nat @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(531,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(1928,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(1215,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ ( c_1 @ c_NatArith_Oof__nat ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
thf(866,plain,
! [A: $i] :
( ( ( A @ ( c_1 @ c_NatArith_Oof__nat ) )
= c_1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(469,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(1796,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)],[469]) ).
thf(565,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(2002,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)],[565]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(1201,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(666,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
thf(2205,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(516,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(1896,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)],[516]) ).
thf(659,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(2190,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(615,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_set @ ( C @ ( E @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( E @ ( D @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro_0) ).
thf(2103,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_set @ ( C @ ( E @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( E @ ( D @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(278,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(1405,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)],[278]) ).
thf(142,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(1104,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)],[142]) ).
thf(422,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(1697,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(204,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(1242,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(641,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(2154,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)],[641]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
thf(1521,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(498,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_22) ).
thf(1863,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(569,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(2011,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)],[569]) ).
thf(781,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(2473,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)],[781]) ).
thf(293,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(1438,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)],[293]) ).
thf(64,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(925,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(163,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(1153,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)],[163]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_IntDef_Oint @ c_IntDef_Oof__int ) )
= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
thf(1338,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_IntDef_Oint @ c_IntDef_Oof__int ) )
= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(463,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(1783,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(183,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(1199,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)],[183]) ).
thf(646,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(2164,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)],[646]) ).
thf(308,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(1470,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_IntDef_Oneg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(427,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(1708,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)],[427]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
thf(1311,plain,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(713,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(2307,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)],[713]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
thf(1067,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(441,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(1736,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)],[441]) ).
thf(456,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
thf(1768,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(501,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
thf(1868,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(743,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(2382,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(117,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(1047,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)],[117]) ).
thf(438,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(1730,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)],[438]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(122,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(1057,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)],[122]) ).
thf(218,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(1274,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)],[218]) ).
thf(694,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(2264,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(136,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(1091,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)],[136]) ).
thf(763,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(2428,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(825,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(115,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(1042,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)],[115]) ).
thf(35,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(862,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)],[35]) ).
thf(630,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(2133,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)],[630]) ).
thf(193,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(1217,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)],[193]) ).
thf(317,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(1487,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(629,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(2132,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(750,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(2396,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)],[750]) ).
thf(202,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(1238,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)],[202]) ).
thf(269,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(1387,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(434,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
thf(1723,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
thf(957,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(195,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(1223,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)],[195]) ).
thf(700,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(2277,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)],[700]) ).
thf(253,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(1355,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)],[253]) ).
thf(365,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(1580,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)],[365]) ).
thf(325,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(1502,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)],[325]) ).
thf(449,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(1751,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)],[449]) ).
thf(480,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(1824,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)],[480]) ).
thf(3,negated_conjecture,
t_d @ ( v_x @ v_A @ ( v_xa @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(788,plain,
t_d @ ( v_x @ v_A @ ( v_xa @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
thf(1883,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(356,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(1560,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)],[356]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(527,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(1920,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(765,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
thf(2433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(551,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(1968,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)],[551]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ c_IntDef_Oint @ c_IntDef_Onat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
thf(1178,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ c_IntDef_Onat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(302,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(1457,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)],[302]) ).
thf(21,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(830,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)],[21]) ).
thf(47,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(889,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(729,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(2345,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)],[729]) ).
thf(221,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(1281,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)],[221]) ).
thf(677,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(2228,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(620,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(2112,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)],[620]) ).
thf(362,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(1573,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(777,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro2_0) ).
thf(2464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(536,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
thf(1938,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
thf(1032,plain,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(486,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(1837,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)],[486]) ).
thf(376,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(1602,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)],[376]) ).
thf(190,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(1210,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)],[190]) ).
thf(404,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_13) ).
thf(1656,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
thf(1079,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(108,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(1027,plain,
! [A: $i] :
( ( A = c_0 )
| ( ( A @ c_IntDef_Oint )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(670,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(2213,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)],[670]) ).
thf(181,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(1195,plain,
( ( tc_IntDef_Oint @ ( c_0 @ c_IntDef_Oint @ c_uminus ) )
= ( c_0 @ c_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(669,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(2211,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(279,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(1407,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)],[279]) ).
thf(443,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(1740,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(522,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(1910,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(27,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(842,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)],[27]) ).
thf(135,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(1089,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)],[135]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(1983,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(159,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(1143,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_IntDef_Oint @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(75,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(948,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)],[75]) ).
thf(468,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(1794,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)],[468]) ).
thf(472,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(1804,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)],[472]) ).
thf(734,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
thf(2359,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= ( A @ ( C @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
thf(1064,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= ( A @ ( C @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(1856,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(368,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(1587,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)],[368]) ).
thf(287,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(1425,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(412,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(1672,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)],[412]) ).
thf(506,axiom,
tc_IntDef_Oint @ class_HOL_Otimes,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
thf(1878,plain,
tc_IntDef_Oint @ class_HOL_Otimes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(432,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(1719,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(93,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(989,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)],[93]) ).
thf(453,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
thf(1762,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(613,axiom,
! [A: $i] :
( ( A @ ( c_IntDef_ONats @ ( c_1 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
thf(2100,plain,
! [A: $i] :
( ( A @ ( c_IntDef_ONats @ ( c_1 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(493,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_1 @ c_uminus ) @ c_Nat_Opower ) ) )
= ( A @ ( c_1 @ c_uminus ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
thf(1851,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_1 @ c_uminus ) @ c_Nat_Opower ) ) )
= ( A @ ( c_1 @ c_uminus ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(458,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(1772,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
thf(1259,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(345,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(1540,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(100,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).
thf(1006,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(33,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(857,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)],[33]) ).
thf(274,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
thf(1397,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(359,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(1567,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
thf(884,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(166,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(1160,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)],[166]) ).
thf(720,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(2323,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)],[720]) ).
thf(176,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(1182,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)],[176]) ).
thf(304,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(1461,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(603,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
thf(2080,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(535,axiom,
tc_IntDef_Oint @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(1937,plain,
tc_IntDef_Oint @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(512,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(1889,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)],[512]) ).
thf(113,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(1039,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(775,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(2460,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)],[775]) ).
thf(320,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(1493,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)],[320]) ).
thf(417,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(1683,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)],[417]) ).
thf(549,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(1964,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)],[549]) ).
thf(538,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
thf(1942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
thf(1292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(68,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(933,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(715,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(2312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(773,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(2455,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)],[773]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_insert ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_insert ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(590,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(2053,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)],[590]) ).
thf(474,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(1810,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)],[474]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(2172,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(618,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(2108,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(297,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(1446,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)],[297]) ).
thf(104,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(1016,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)],[104]) ).
thf(188,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(1207,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(717,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(2317,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)],[717]) ).
thf(164,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(1155,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)],[164]) ).
thf(445,axiom,
tc_nat @ class_HOL_Otimes,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).
thf(1744,plain,
tc_nat @ class_HOL_Otimes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(703,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(2285,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)],[703]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ c_NatArith_Oof__nat ) )
= ( A @ ( c_1 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_plus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ c_NatArith_Oof__nat ) )
= ( A @ ( c_1 @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_plus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(228,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(1297,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(340,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( C @ c_in ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
thf(1530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( C @ c_in ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(553,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
thf(1974,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(352,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(1552,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)],[352]) ).
thf(123,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(1060,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)],[123]) ).
thf(470,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(1799,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)],[470]) ).
thf(504,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(1874,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)],[504]) ).
thf(289,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(1429,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)],[289]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
thf(1715,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(698,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(2272,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)],[698]) ).
thf(272,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
thf(1393,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(96,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(997,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(162,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(1150,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)],[162]) ).
thf(313,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(1478,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)],[313]) ).
thf(215,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(1266,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)],[215]) ).
thf(746,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(2387,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)],[746]) ).
thf(483,axiom,
tc_nat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(1831,plain,
tc_nat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
thf(1231,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(533,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(1932,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)],[533]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).
thf(984,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_NatArith_Oof__nat ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(374,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(1599,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(206,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(1246,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)],[206]) ).
thf(390,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(1627,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)],[390]) ).
thf(338,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(1525,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(244,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(1333,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)],[244]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
thf(1434,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ c_uminus ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ c_uminus ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(585,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(2043,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(921,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(111,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(1035,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)],[111]) ).
thf(128,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(1071,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)],[128]) ).
thf(515,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
thf(1895,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(384,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(1616,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(761,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(2423,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)],[761]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ ( C @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ ( C @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(792,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(665,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(2203,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(668,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(2208,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)],[668]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_IntDef_ONats @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
thf(2057,plain,
! [B: $i,A: $i] :
( ( A @ ( c_IntDef_ONats @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(491,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(1846,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)],[491]) ).
thf(178,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(1187,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)],[178]) ).
thf(768,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(2440,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)],[768]) ).
thf(755,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(2408,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)],[755]) ).
thf(607,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_0) ).
thf(2089,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(794,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(726,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(2338,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)],[726]) ).
thf(563,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(1996,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)],[563]) ).
thf(330,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(1510,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(748,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(2391,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)],[748]) ).
thf(447,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
thf(1747,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
thf(1548,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(578,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(2028,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(392,axiom,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(1631,plain,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(692,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(2260,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_OatLeastAtMost ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_OatLeastAtMost ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(520,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(1906,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)],[520]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(400,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(1648,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(454,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
thf(1764,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(757,axiom,
! [A: $i] :
( ( A @ ( c_IntDef_ONats @ ( c_0 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
thf(2413,plain,
! [A: $i] :
( ( A @ ( c_IntDef_ONats @ ( c_0 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(689,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(2253,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)],[689]) ).
thf(699,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(2275,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)],[699]) ).
thf(580,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(2033,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
thf(2149,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(525,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
thf(1916,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(383,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(1615,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(151,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(1125,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)],[151]) ).
thf(658,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(2188,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(386,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
thf(1620,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(749,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(2393,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)],[749]) ).
thf(571,axiom,
tc_nat @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(2016,plain,
tc_nat @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) )
= ( C @ tc_set @ ( D @ ( B @ c_minus ) ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
thf(1388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) )
= ( C @ tc_set @ ( D @ ( B @ c_minus ) ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(343,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(1535,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)],[343]) ).
thf(277,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(1403,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)],[277]) ).
thf(335,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(1520,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(211,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(1256,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)],[211]) ).
thf(402,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(1652,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)],[402]) ).
thf(532,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(1929,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)],[532]) ).
thf(424,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(1701,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)],[424]) ).
thf(751,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(2398,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)],[751]) ).
thf(157,axiom,
~ ( tc_IntDef_Oint @ ( c_1 @ c_Parity_Oeven ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
thf(1139,plain,
~ ( tc_IntDef_Oint @ ( c_1 @ c_Parity_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(410,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(1669,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(721,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(2326,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)],[721]) ).
thf(2,negated_conjecture,
! [A: $i] : ( t_b @ ( A @ v_h @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(787,plain,
! [A: $i] : ( t_b @ ( A @ v_h @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(499,axiom,
tc_IntDef_Oint @ class_Power_Orecpower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(1865,plain,
tc_IntDef_Oint @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(394,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(1635,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)],[394]) ).
thf(143,axiom,
tc_IntDef_Oint @ ( c_0 @ c_Parity_Oeven ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
thf(1107,plain,
tc_IntDef_Oint @ ( c_0 @ c_Parity_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(243,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(1332,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(591,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(2055,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)],[591]) ).
thf(647,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(2166,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)],[647]) ).
thf(413,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(1675,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)],[413]) ).
thf(217,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(1271,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)],[217]) ).
thf(262,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(1371,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(774,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(2457,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)],[774]) ).
thf(61,axiom,
( ( c_0 @ c_IntDef_Onat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
thf(919,plain,
( ( c_0 @ c_IntDef_Onat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(637,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(2148,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(718,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(2319,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)],[718]) ).
thf(735,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( D @ ( C @ c_times ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono3_0) ).
thf(2361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( D @ ( C @ c_times ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(623,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(2119,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)],[623]) ).
thf(53,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(900,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)],[53]) ).
thf(783,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(2478,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(605,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_1 @ c_uminus ) @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
thf(2084,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( c_1 @ c_uminus ) @ c_Nat_Opower ) ) )
= c_1 )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(758,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(2415,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)],[758]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
thf(1011,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(346,axiom,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
thf(1542,plain,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_NatArith_Oof__nat ) )
= ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_plus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
thf(1122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_NatArith_Oof__nat ) )
= ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_plus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(741,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(2378,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)],[741]) ).
thf(662,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(2197,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)],[662]) ).
thf(173,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(1175,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)],[173]) ).
thf(639,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(2151,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(678,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(2229,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)],[678]) ).
thf(251,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(1349,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)],[251]) ).
thf(611,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(2097,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(691,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(2257,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)],[691]) ).
thf(369,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(1589,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)],[369]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
thf(2246,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(709,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(2299,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)],[709]) ).
thf(43,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(880,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)],[43]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(1801,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(361,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(1571,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(1376,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(505,axiom,
tc_IntDef_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(1877,plain,
tc_IntDef_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(479,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(1821,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)],[479]) ).
thf(167,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(1162,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)],[167]) ).
thf(770,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(2446,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)],[770]) ).
thf(30,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(848,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)],[30]) ).
thf(240,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(1325,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)],[240]) ).
thf(50,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(895,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(249,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(1344,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(1112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(48,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(890,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)],[48]) ).
thf(409,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_6) ).
thf(1667,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(654,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(2180,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)],[654]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OlessThan ) @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_minus ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OlessThan ) @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_minus ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(655,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( B @ c_NatArith_Oof__nat ) @ c_IntDef_Oof__int ) )
= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
thf(2182,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( B @ c_NatArith_Oof__nat ) @ c_IntDef_Oof__int ) )
= ( A @ ( B @ c_NatArith_Oof__nat ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(628,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(2129,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)],[628]) ).
thf(728,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(2343,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)],[728]) ).
thf(354,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
thf(1556,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(705,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( D @ c_times ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono4_0) ).
thf(2289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( D @ c_times ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(106,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(1022,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)],[106]) ).
thf(722,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(2329,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)],[722]) ).
thf(67,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(932,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(543,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(1952,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)],[543]) ).
thf(171,axiom,
( ( tc_nat @ ( c_0 @ c_SetInterval_OlessThan ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
thf(1171,plain,
( ( tc_nat @ ( c_0 @ c_SetInterval_OlessThan ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(488,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(1841,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)],[488]) ).
thf(731,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(2350,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)],[731]) ).
thf(79,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(959,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)],[79]) ).
thf(20,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(827,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)],[20]) ).
thf(589,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
thf(2051,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(397,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(1643,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)],[397]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_ONats @ ( A @ ( B @ ( C @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
thf(2139,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_ONats @ ( A @ ( B @ ( C @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(2244,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(575,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(2022,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(711,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(2303,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(141,axiom,
( ( c_0 @ c_IntDef_Oint )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
thf(1102,plain,
( ( c_0 @ c_IntDef_Oint )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(642,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(2156,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)],[642]) ).
thf(667,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(2207,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(421,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
thf(1694,plain,
c_0 != c_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(598,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(2069,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)],[598]) ).
thf(357,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(1562,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)],[357]) ).
thf(90,axiom,
tc_nat @ ( c_0 @ c_Parity_Oeven ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
thf(983,plain,
tc_nat @ ( c_0 @ c_Parity_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(601,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(2075,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)],[601]) ).
thf(759,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(2418,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)],[759]) ).
thf(423,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(1699,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)],[423]) ).
thf(752,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(2401,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)],[752]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( C @ ( B @ c_times ) ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
thf(1594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( C @ ( B @ c_times ) ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(596,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
thf(2064,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(738,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(2369,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)],[738]) ).
thf(436,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
thf(1726,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(258,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(1364,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)],[258]) ).
thf(208,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(1250,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)],[208]) ).
thf(541,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
thf(1948,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(683,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
thf(2239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(366,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(1583,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)],[366]) ).
thf(407,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(1662,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)],[407]) ).
thf(625,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(2124,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)],[625]) ).
thf(132,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(1081,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)],[132]) ).
thf(560,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(1990,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)],[560]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(309,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(1472,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(546,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
thf(1958,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(24,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(836,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)],[24]) ).
thf(118,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(1049,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)],[118]) ).
thf(566,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(2005,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)],[566]) ).
thf(130,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(1076,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)],[130]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
thf(1758,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(169,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(1166,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)],[169]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(189,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(1208,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)],[189]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( C @ ( B @ c_minus ) ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_minus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( C @ ( B @ c_minus ) ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_minus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(582,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(2037,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)],[582]) ).
thf(771,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(2449,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)],[771]) ).
thf(329,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(1509,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(724,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(2333,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(160,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(1145,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)],[160]) ).
thf(349,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(1547,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(457,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(1770,plain,
( ( c_0 @ c_Suc )
= ( tc_nat @ ( c_1 @ ( c_1 @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(32,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(855,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(333,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(1516,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)],[333]) ).
thf(107,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(1025,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)],[107]) ).
thf(85,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(971,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)],[85]) ).
thf(634,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
thf(2143,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(399,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(1647,plain,
tc_IntDef_Oint @ ( c_1 @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(651,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(2175,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)],[651]) ).
thf(462,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(1780,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)],[462]) ).
thf(644,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(2160,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)],[644]) ).
thf(381,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1611,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(740,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(2375,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)],[740]) ).
thf(196,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(1225,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)],[196]) ).
thf(594,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(2060,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(444,axiom,
tc_nat @ class_Power_Orecpower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(1743,plain,
tc_nat @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(660,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
thf(2192,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(46,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(887,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)],[46]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( C @ ( B @ c_plus ) ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_plus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( C @ ( B @ c_plus ) ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_plus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(209,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_NatArith_Oof__nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
thf(1252,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_NatArith_Oof__nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(464,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(1785,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)],[464]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
thf(1235,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(236,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(1317,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)],[236]) ).
thf(405,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(1658,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(415,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
thf(1679,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(586,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(2044,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
thf(1130,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(442,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(1738,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)],[442]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(56,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(907,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
thf(1711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(120,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(1053,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)],[120]) ).
thf(323,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(1499,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(466,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(1790,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)],[466]) ).
thf(675,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(2224,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(229,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(1300,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)],[229]) ).
thf(300,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(1452,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)],[300]) ).
thf(395,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(1637,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)],[395]) ).
thf(673,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(2219,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)],[673]) ).
thf(627,axiom,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(2128,plain,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(344,axiom,
( ( tc_nat @ ( c_0 @ c_SetInterval_OatLeast ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
thf(1538,plain,
( ( tc_nat @ ( c_0 @ c_SetInterval_OatLeast ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(76,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(951,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(779,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_ONats @ ( A @ ( B @ ( C @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
thf(2468,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_ONats @ ( A @ ( B @ ( C @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_ONats @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(194,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(1220,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(254,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(1358,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(534,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(1934,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)],[534]) ).
thf(756,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ ( C @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
thf(2411,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_IntDef_OInts @ ( A @ ( B @ ( C @ c_times ) ) @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( C @ c_in ) ) )
| ~ ( A @ ( c_IntDef_OInts @ ( B @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(492,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(1849,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)],[492]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(36,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(864,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)],[36]) ).
thf(448,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(1749,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(411,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(1670,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(508,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(1881,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)],[508]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(1240,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(347,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(1543,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)],[347]) ).
thf(455,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(1766,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(158,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(1141,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)],[158]) ).
thf(762,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(2426,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)],[762]) ).
thf(556,axiom,
( ( tc_nat @ ( c_0 @ c_SetInterval_OatMost ) )
= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
thf(1981,plain,
( ( tc_nat @ ( c_0 @ c_SetInterval_OatMost ) )
= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_SetsAndFunctions_Oelt__set__times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__one__times_0) ).
thf(1955,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_SetsAndFunctions_Oelt__set__times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(635,axiom,
tc_nat @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(2145,plain,
tc_nat @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(316,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(1485,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(327,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
thf(1506,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(431,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(1717,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)],[431]) ).
thf(579,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(2030,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)],[579]) ).
thf(695,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(2266,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(537,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(1940,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
thf(1421,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(487,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
thf(1839,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(784,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(2479,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(303,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(1459,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)],[303]) ).
thf(175,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(1180,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)],[175]) ).
thf(550,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(1966,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(661,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(2194,plain,
! [A: $i] :
( ( c_1 != c_0 )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(671,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(2215,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)],[671]) ).
thf(500,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
thf(1866,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(144,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(1108,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)],[144]) ).
thf(766,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(2435,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)],[766]) ).
thf(29,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(845,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)],[29]) ).
thf(526,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(1918,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)],[526]) ).
thf(401,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(1649,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)],[401]) ).
thf(133,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(1084,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)],[133]) ).
thf(602,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
thf(2078,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
thf(1321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(524,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(1913,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)],[524]) ).
thf(714,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
thf(2310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
thf(976,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(1844,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(54,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(903,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(730,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(2347,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)],[730]) ).
thf(403,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(1654,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)],[403]) ).
thf(281,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(1412,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)],[281]) ).
thf(298,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(1448,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)],[298]) ).
thf(657,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(2187,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(619,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(2110,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(712,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(2305,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(363,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(1575,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)],[363]) ).
thf(224,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(1289,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ ( A @ c_div ) ) )
= c_1 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(28,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(844,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(676,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
thf(2226,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(440,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(1734,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(473,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(1807,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)],[473]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(769,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(2443,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)],[769]) ).
thf(81,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(963,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)],[81]) ).
thf(754,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(2406,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(314,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(1481,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_IntDef_Oint @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(74,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(946,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(391,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
thf(1629,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(446,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(1745,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)],[446]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(1854,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(205,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(1244,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)],[205]) ).
thf(337,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(1523,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)],[337]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] : ( t_b @ ( B @ ( A @ v_l ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(786,plain,
! [B: $i,A: $i] : ( t_b @ ( B @ ( A @ v_l ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(80,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(961,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)],[80]) ).
thf(268,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(1385,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)],[268]) ).
thf(433,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(1721,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(747,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(2389,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)],[747]) ).
thf(312,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(1476,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)],[312]) ).
thf(247,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(1341,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(612,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
thf(2098,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(124,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(1062,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)],[124]) ).
thf(328,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(1508,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(355,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
thf(1558,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(640,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(2152,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( c_1 @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(693,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(2262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ c_IntDef_Oof__int ) )
= ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_uminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(584,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(2041,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)],[584]) ).
thf(460,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(1777,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(294,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(1440,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_div ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(232,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(1308,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)],[232]) ).
thf(597,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(2066,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)],[597]) ).
thf(645,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(2162,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(191,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(1212,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)],[191]) ).
thf(378,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(1607,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(52,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(899,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)],[52]) ).
thf(716,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
thf(2315,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(562,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(1994,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)],[562]) ).
thf(573,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(2019,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)],[573]) ).
thf(116,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(1045,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)],[116]) ).
thf(109,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(1030,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)],[109]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(1491,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(744,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(2384,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)],[744]) ).
thf(782,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(2475,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)],[782]) ).
thf(226,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(1294,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(776,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(2462,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)],[776]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
thf(2095,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(22,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(832,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)],[22]) ).
thf(514,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(1893,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)],[514]) ).
thf(707,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(2294,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)],[707]) ).
thf(296,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(1444,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)],[296]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
thf(1442,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(760,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(2421,plain,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(10,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
thf(800,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(521,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
thf(1908,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(435,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(1725,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
thf(1578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(745,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(2385,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)],[745]) ).
thf(690,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(2255,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(83,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(967,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_div ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(139,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(1097,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)],[139]) ).
thf(680,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(2233,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)],[680]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
thf(1303,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(339,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(1527,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)],[339]) ).
thf(207,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(1248,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)],[207]) ).
thf(97,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(999,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)],[97]) ).
thf(704,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(2287,plain,
! [A: $i] :
( ~ ( A @ ( c_0 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(396,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(1642,plain,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(614,axiom,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(2102,plain,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(331,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(1512,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)],[331]) ).
thf(459,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(1774,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(273,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(1395,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)],[273]) ).
thf(389,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(1625,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(371,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(1593,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(292,axiom,
( c_1
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(1436,plain,
( c_1
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(664,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(2201,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)],[664]) ).
thf(257,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(1363,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)],[257]) ).
thf(13,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(807,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)],[13]) ).
thf(51,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(897,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)],[51]) ).
thf(737,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(2366,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)],[737]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_NatArith_Oof__nat ) @ ( A @ ( B @ c_NatArith_Oof__nat ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(608,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(2091,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)],[608]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(1891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(1473,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(8,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(796,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)],[8]) ).
thf(477,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(1816,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(321,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Otimes )
| ( A @ tc_set @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_6) ).
thf(1495,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Otimes )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(574,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(2021,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(380,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(1610,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(252,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(1352,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)],[252]) ).
thf(482,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(1829,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)],[482]) ).
thf(764,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(2430,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)],[764]) ).
thf(105,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(1019,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)],[105]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(529,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(1923,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(18,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(822,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)],[18]) ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
thf(1925,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(518,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(1902,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)],[518]) ).
thf(510,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(1885,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(39,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(871,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)],[39]) ).
thf(149,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(1120,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)],[149]) ).
thf(739,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(2372,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
thf(1093,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(732,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(2353,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)],[732]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
thf(839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(684,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(2241,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)],[684]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
thf(987,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(481,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
thf(1827,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(213,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(1261,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)],[213]) ).
thf(341,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(1532,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
thf(860,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(554,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(1976,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(351,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(1550,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(31,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(850,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(429,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(1713,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)],[429]) ).
thf(373,axiom,
! [A: $i] :
( ( A @ ( c_IntDef_OInts @ ( c_1 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
thf(1597,plain,
! [A: $i] :
( ( A @ ( c_IntDef_OInts @ ( c_1 @ c_in ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(1004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(326,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(1505,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(275,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(1399,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)],[275]) ).
thf(697,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
thf(2270,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
thf(1621,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(237,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(1320,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(63,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(923,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)],[63]) ).
thf(593,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(2059,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(283,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(1416,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)],[283]) ).
thf(649,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
thf(2170,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(127,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(1069,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(502,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
thf(1870,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(719,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(2321,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)],[719]) ).
thf(539,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_14) ).
thf(1944,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(260,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(1367,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)],[260]) ).
thf(69,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(935,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)],[69]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
thf(1009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(416,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
thf(1681,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(177,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(1184,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)],[177]) ).
thf(600,axiom,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(2074,plain,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(305,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(1463,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)],[305]) ).
thf(358,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(1565,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)],[358]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(1037,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(708,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(2297,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)],[708]) ).
thf(767,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(2438,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)],[767]) ).
thf(682,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(2238,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(186,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(1204,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)],[186]) ).
thf(475,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(1812,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)],[475]) ).
thf(617,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
thf(2106,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
thf(2087,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
thf(1468,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_NatArith_Oof__nat ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(780,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(2470,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)],[780]) ).
thf(44,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(882,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)],[44]) ).
thf(652,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(2177,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(8618,plain,
$false,
inference(e,[status(thm)],[1879,2094,2341,1454,2072,1237,909,1899,893,1315,941,2331,1950,2199,1665,1586,1501,2452,809,1369,1190,1818,1295,2280,1554,1110,1686,2250,2363,1158,2117,2231,2062,1618,994,1401,1073,2014,1728,1692,1305,1173,1569,2248,873,1205,2282,1591,2114,1269,878,2380,1971,1793,1533,1608,1137,1756,2035,2141,1872,1233,2168,1988,1342,1954,2146,930,1497,1705,1788,1426,1164,1999,814,1327,1095,1835,2216,1001,2046,1127,1391,841,973,1613,2010,1359,1601,2082,1475,1366,1887,1645,1921,2136,1904,1518,1703,1228,1623,1482,1254,1287,1985,2039,785,2269,1323,917,802,1313,2185,1832,1992,1132,2356,1055,1409,1760,1660,1330,1860,2466,2126,1545,817,1379,1147,2049,1013,1115,2158,2024,2301,1778,2403,1087,1514,969,1347,1362,1963,2007,1489,2027,789,1373,1911,834,1978,937,1677,1960,1051,2178,2222,1946,1465,2105,1450,1040,1632,1418,2236,1858,2122,2291,1383,2335,966,2017,905,981,1843,1169,1928,1215,866,1796,2002,1201,2205,1896,2190,2103,1405,1104,1697,1242,2154,1521,1863,2011,2473,1438,925,1153,1338,1783,1199,2164,1470,1708,1311,2307,1067,1736,1768,1868,2382,1047,1730,798,1057,1274,2264,1091,2428,825,1042,862,2133,1217,1487,2132,2396,1238,1387,1723,957,1223,2277,1355,1580,1502,1751,1824,788,1883,1560,1423,1920,2433,1968,1178,1457,830,889,2345,1281,2228,2112,1573,2464,1938,1032,1837,1602,1210,1656,1079,1027,2213,1195,2211,1407,1740,1910,842,1089,1983,1143,948,1794,1804,2359,1064,1856,1587,1425,1672,1878,1719,869,989,1762,2100,1851,1772,1259,1540,1006,857,1397,1567,884,1160,2323,1182,1461,2080,1937,1889,1039,2460,1493,1683,1964,1942,1292,933,2312,2455,1414,2053,1810,2172,2108,1446,1016,1207,2317,1155,1744,2285,1099,1297,1530,1974,1552,1060,1799,1874,1429,1715,2272,1393,1263,997,1150,1478,1266,2387,1831,1231,1192,1932,984,911,1599,1246,1627,1525,1333,1434,1814,2043,921,1035,1071,1895,1616,2423,1732,792,2203,2208,805,2057,1846,1187,2440,2408,2089,794,2338,1996,1510,2391,1747,1548,2028,1631,2260,1278,1906,1135,1648,1764,2413,2253,2275,2033,2149,1916,1615,1125,2188,1620,2393,2016,1388,1535,1403,1520,1256,1652,1929,1701,2398,1139,1669,2326,787,1865,1635,1107,1332,2055,2166,1675,1271,1371,2457,919,2148,2319,2361,2119,900,2478,2084,2415,1117,1011,1542,1122,2378,2197,1175,2151,2229,1349,2097,2257,1589,2246,2299,880,1801,1571,1376,1877,1821,1162,2446,848,1325,895,1344,1112,890,1667,2180,811,2182,2129,2343,1556,2289,943,1022,2329,932,1952,1171,1841,2350,959,827,2051,1643,2139,2244,2022,2303,1102,2156,2207,1694,2069,1562,983,2075,2418,1699,2401,1594,2064,2369,1726,1364,1250,1948,2239,1583,1662,2124,1081,1990,939,1472,1958,836,1049,2005,1076,1758,1166,1203,1208,927,2037,2449,1509,2333,1145,1547,1770,855,1516,1025,971,2143,1605,1647,2175,1780,2160,1611,2375,1225,2060,1743,2192,887,954,1252,1785,1235,1317,1658,1679,2044,1130,1738,1336,907,1711,1053,1499,1790,2224,1300,1452,1637,2219,2128,1538,951,2468,1220,1358,1934,2411,1849,1284,864,1749,978,1670,1881,1240,1543,1766,1141,2426,1981,1955,2145,1485,1506,1717,2030,2266,876,1940,1421,1839,2479,1459,1180,1966,2194,2215,1866,1108,2435,845,1918,1649,1084,2078,1321,1913,2310,976,1844,903,2347,1654,1412,1448,2187,2110,2305,1575,1289,844,2226,1734,1807,1276,2443,963,2406,1481,946,1629,1745,1854,1244,1523,786,961,1385,1721,2389,1476,1341,2098,1062,1508,1558,2152,2262,1689,914,2041,1777,1440,1308,2066,2162,1212,1607,899,2315,1994,2019,1045,1030,1491,2384,2475,1294,2462,2095,832,1893,2294,1444,1442,2421,800,1908,1725,1578,2385,2255,967,1097,2233,1303,1527,1248,999,2287,1642,2102,1512,1774,1395,1625,1593,1380,1436,2201,1363,807,897,2366,1197,2091,1891,1473,796,1816,1495,2021,1610,1352,1829,2430,1019,992,1923,822,1925,1902,1885,871,1120,2372,1093,2353,839,2241,987,1827,1261,1532,860,1976,1550,850,1713,1597,1431,1004,1505,1399,2270,1621,1320,923,2059,1416,2170,1069,1870,2321,1944,1367,935,1009,1681,1184,2074,1463,1565,1037,2297,2438,2238,1204,1812,2106,2087,1468,2470,882,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA044-1 : 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 : n017.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 22:05:20 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.86/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.35/1.46 % [INFO] Parsing done (495ms).
% 2.35/1.48 % [INFO] Running in sequential loop mode.
% 3.23/1.86 % [INFO] eprover registered as external prover.
% 3.23/1.86 % [INFO] Scanning for conjecture ...
% 4.28/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 2783 axioms. Running axiom selection ...
% 6.29/2.60 % [INFO] Axiom selection finished. Selected 779 axioms (removed 2004 axioms).
% 6.87/2.87 % [INFO] Problem is propositional (TPTP CNF).
% 6.87/2.89 % [INFO] Type checking passed.
% 6.87/2.89 % [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 ...
% 51.59/11.39 % External prover 'e' found a proof!
% 51.59/11.39 % [INFO] Killing All external provers ...
% 51.59/11.39 % Time passed: 10871ms (effective reasoning time: 9902ms)
% 46.38/11.40 % Axioms used in derivation (779): cls_IntDef_Ozero__less__int__conv_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_Set_OPow__UNIV_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Power_Opower__0__Suc_0, cls_Set_OPow__iff_1, cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, cls_Parity_Opower__less__zero__eq__number__of_0, clsrel_Ring__and__Field_Opordered__comm__semiring_14, cls_Parity_Opower__le__zero__eq__number__of_1, clsrel_Ring__and__Field_Opordered__semiring_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_Nat_Onot__less0_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_Nat_Oone__eq__mult__iff_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6, cls_NatArith_Oadd__diff__assoc2_0, cls_SetInterval_OgreaterThanLessThan__iff_0, cls_NatArith_Oof__nat__0__le__iff_0, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_Power_Onat__zero__less__power__iff_2, cls_SetInterval_OgreaterThanAtMost__iff_2, cls_Set_Osingleton__insert__inj__eq_0, cls_Parity_Oeven__nat__power_2, cls_IntDef_Ozless__int_0, cls_SetInterval_OatMost__0_0, clsarity_nat_32, cls_IntDef_Oint__eq__0__conv_1, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17, cls_Parity_Oeven__sum_2, cls_Set_OUNIV__not__empty_0, cls_Set_OsubsetI_1, clsrel_Ring__and__Field_Oordered__semidom_2, cls_Nat_Onat__add__left__cancel__less_1, clsrel_Ring__and__Field_Oordered__semidom_16, cls_IntDef_Ozless__nat__conj_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, 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_NatArith_Oof__nat__mult_0, clsrel_OrderedGroup_Olordered__ab__group_9, clsrel_Ring__and__Field_Oordered__ring__strict_26, cls_IntDiv_Ozdiv__1_0, cls_IntDef_Oint__nat__eq_0, clsrel_Ring__and__Field_Oordered__semidom_39, cls_Set_ODiff__cancel_0, clsrel_Ring__and__Field_Oordered__idom_12, cls_Set_Osubset__UNIV_0, clsrel_Ring__and__Field_Ofield_8, cls_Set_Oinsert__Diff1_0, cls_Nat_Omult__le__cancel1_1, cls_Parity_Oeven__nat__product_1, clsrel_OrderedGroup_Omonoid__mult_2, cls_NatArith_Oof__nat__0__eq__iff_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_Ring__and__Field_Oordered__semidom_34, cls_OrderedGroup_Opprt__eq__id_0, cls_Parity_Oeven__nat__sum_1, cls_Finite__Set_OFinites_OemptyI_0, cls_IntDef_Oof__int__of__nat__eq_0, cls_Nat_OSuc__Suc__eq_0, clsarity_nat_40, cls_NatArith_Oof__nat__add_0, 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_Orderings_Oorder__less__irrefl_0, cls_Parity_Ozero__less__power__eq__number__of_1, cls_IntDef_Oint__Suc_0, cls_IntDiv_Ozero__less__zpower__abs__iff_2, cls_OrderedGroup_Oabs__ge__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_NatArith_Oof__nat__less__iff_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, cls_SetInterval_OatLeast__iff_1, cls_Set_Osingleton__inject__dest_0, clsrel_OrderedGroup_Olordered__ab__group__abs_18, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_Finite__Set_OFinites_OinsertI_0, cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, 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_Set_OCompl__iff_1, cls_IntDef_Onegative__eq__positive_0, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__0__eq_0, cls_IntDef_OInts__0_0, clsarity_IntDef__Oint_56, cls_Parity_Opower__minus__even_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_IntDef_Oint__less__0__conv_0, cls_OrderedGroup_Onprt__mono_0, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_Nat_Oadd__is__0_0, clsarity_set_2, cls_IntDiv_ODIVISION__BY__ZERO_0, clsarity_nat_3, clsrel_Power_Orecpower_24, clsarity_IntDef__Oint_3, cls_NatBin_Oeq__0__number__of_1, cls_NatArith_Oof__nat__less__0__iff_0, cls_Ring__and__Field_Omult__cancel__left1_2, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Onat__le__0_0, cls_SetInterval_OatMost__iff_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Nat_Ozero__less__diff_1, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_IntDiv_Ozmod__zmult__self2_0, clsrel_Ring__and__Field_Ocomm__ring__1_7, cls_OrderedGroup_Oneg__meet__eq__join_0, cls_SetInterval_Ofinite__atLeastLessThan__int_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, clsrel_OrderedGroup_Olordered__ab__group__meet_9, cls_Power_Opower__one__right_0, cls_Set_OPow__iff_0, cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0, cls_SetsAndFunctions_Oset__times__intro2_0, cls_IntDef_Oof__int__less__iff_0, clsarity_nat_29, clsrel_Ring__and__Field_Ocomm__ring__1_24, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_Nat_Omult__less__cancel2_1, cls_IntDef_OInts__add_0, cls_NatArith_Odiff__diff__right_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_SetsAndFunctions_Oset__times__mono2_0, cls_Set_OpsubsetI_0, cls_Set_Osubset__refl_0, cls_IntDef_Oof__nat__in__Nats_0, cls_Divides_Odiv__mult__self__is__m_0, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1, cls_Set_ODiff__UNIV_0, cls_Parity_Oeven__power_2, cls_Nat_Omult__0__right_0, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Set_OCompl__eq__Compl__iff_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_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, 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cls_Divides_ODIVISION__BY__ZERO__MOD_0, cls_IntDiv_Ozero__le__zpower__abs_0, cls_IntDiv_Ozdiv__self_0, cls_Finite__Set_Ofinite__Diff_0, cls_SetInterval_OatMost__subset__iff_0, cls_SetInterval_OlessThan__0_0, clsrel_Ring__and__Field_Oordered__idom_0, clsrel_OrderedGroup_Olordered__ab__group__abs_7, cls_IntDiv_Ozdiv__zmult__self2_0, clsrel_Ring__and__Field_Oordered__idom_45, cls_Parity_Oeven__nat__Suc_0, 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_Set_ODiff__iff_0, cls_IntDef_Oof__int__0__eq__iff_1, clsarity_IntDef__Oint_30, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, cls_IntDef_Onegative__zle_0, clsarity_nat_13, cls_IntDef_Oof__int__int__eq_0, clsrel_Ring__and__Field_Oordered__semidom_29, cls_Ring__and__Field_Omult__zero__left_0, cls_NatArith_Oof__nat__less__iff_1, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, 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, clsarity_IntDef__Oint_41, 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, clsrel_Ring__and__Field_Opordered__cancel__semiring_4, cls_NatBin_Oone__mod__nat__number__of_1, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsrel_OrderedGroup_Olordered__ab__group__join_9, clsrel_Ring__and__Field_Oordered__idom_6, clsrel_LOrder_Omeet__semilorder_1, clsarity_set_0, clsarity_IntDef__Oint_51, cls_IntArith_Ozle__diff1__eq_1, cls_Nat_OSuc__less__eq_0, cls_Parity_Opower__eq__0__iff__number__of_0, clsarity_nat_4, cls_IntArith_Oone__less__nat__eq_0, clsarity_IntDef__Oint_23, cls_Parity_Oeven__difference_3, clsrel_OrderedGroup_Olordered__ab__group__meet_8, cls_IntDef_Oof__int__diff_0, cls_SetsAndFunctions_Oset__times__mono_0, cls_Nat_Ole0_0, cls_Parity_Oeven__nat__sum_3, clsrel_OrderedGroup_Oab__semigroup__mult_1, clsrel_Ring__and__Field_Ocomm__ring__1_23, 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, cls_NatBin_Oone__div__nat__number__of_0, cls_Set_Oinsert__iff_0, cls_Set_Oinsert__absorb2_0, cls_Nat_Oop_A_L_Oadd__0_0, clsrel_Ring__and__Field_Oordered__semidom_30, cls_IntDiv_Opos__mod__bound_0, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_Nat_Oadd__gr__0_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3, cls_Set_Onot__psubset__empty_0, cls_IntDef_Ozero__less__nat__eq_0, cls_NatArith_Oof__nat__0__eq__iff_0, 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_SetInterval_OgreaterThanAtMost__empty_0, cls_Nat_Ole__0__eq_1, cls_IntArith_Oint__eq__iff__number__of_2, clsarity_IntDef__Oint_50, cls_NatArith_Oof__nat__diff_0, cls_Set_OPow__empty_0, cls_Parity_Opower__minus__odd_0, clsrel_Ring__and__Field_Ocomm__ring__1_12, clsarity_nat_2, clsrel_Ring__and__Field_Ofield_18, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Set_OpsubsetE_1, cls_Nat_Omult__le__cancel2_0, cls_IntDiv_Ozmod__zminus__zminus_0, cls_Nat_OZero__not__Suc_0, cls_Divides_Omod__mult__self__is__0_0, cls_SetInterval_OatMost__subset__iff_1, clsrel_Ring__and__Field_Oordered__ring__strict_2, cls_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, clsrel_OrderedGroup_Olordered__ab__group__meet_2, cls_Set_Osingleton__insert__inj__eq_2, cls_Parity_Ominus__one__odd__power_0, cls_Nat_OlessI_0, cls_IntDef_Oof__int__eq__0__iff_1, cls_SetInterval_Ofinite__atMost_0, cls_SetInterval_OatLeastAtMost__iff_0, cls_Set_Odouble__complement_0, 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_Set_Oinsert__subset_0, cls_Nat_Oone__eq__mult__iff_1, clsrel_Ring__and__Field_Ofield_12, cls_Parity_Opower__even__abs__number__of_0, cls_NatArith_Oof__nat__le__iff_1, 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_IntDef_ONats__mult_0, cls_Nat_Omult__is__0_0, cls_IntDiv_Ozmod__zadd__self1_0, cls_IntDef_Oint__le__0__conv_0, clsrel_Ring__and__Field_Ocomm__ring__1_28, cls_SetInterval_OatLeast__0_0, cls_List_Ochar_Osize_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, clsarity_set_15, cls_List_Odrop__drop_0
% 46.38/11.40 % No. of inferences in proof: 1569
% 46.38/11.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10871 ms resp. 9902 ms w/o parsing
% 53.29/11.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 53.29/11.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------