%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA039-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.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 06:50:21 AM UTC 2026
% Result : Unsatisfiable 132.62s 34.85s
% Output : Refutation 135.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1042
% Syntax : Number of formulae : 2895 ( 521 unt; 0 typ; 2 def)
% Number of atoms : 6435 ( 797 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 16533 (3052 ~;2858 |; 0 &;10623 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 101 ( 98 usr; 9 con; 0-3 aty)
% Number of variables : 3638 ( 0 ^;3634 !; 2 ?;3638 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_h_decl,type,
v_h: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0__cancel_decl,type,
class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Osemigroup__add_decl,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(c_SetInterval_OgreaterThan_decl,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1__cancel_decl,type,
class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0_decl,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(class_HOL_Otimes_decl,type,
class_HOL_Otimes: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_decl,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(class_HOL_Ozero_decl,type,
class_HOL_Ozero: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_HOL_Oone_decl,type,
class_HOL_Oone: $i > $o ).
thf(class_HOL_Oplus_decl,type,
class_HOL_Oplus: $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_SetInterval_OlessThan_decl,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0__cancel_decl,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
thf(class_OrderedGroup_Osemigroup__mult_decl,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_decl,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $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(tc_set_decl,type,
tc_set: $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Ring__and__Field_Olordered__ring_decl,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_Divides_Oop_Advd_decl,type,
c_Divides_Oop_Advd: $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_in_decl,type,
c_in: $i > $i > $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_LOrder_Omeet__semilorder_decl,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_decl,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__abs__if_decl,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_LOrder_Olorder_decl,type,
class_LOrder_Olorder: $i > $o ).
thf(c_SetsAndFunctions_Oelt__set__plus_decl,type,
c_SetsAndFunctions_Oelt__set__plus: $i > $i > $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group_decl,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(c_SetsAndFunctions_Oelt__set__times_decl,type,
c_SetsAndFunctions_Oelt__set__times: $i > $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_1_decl,type,
c_1: $i ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_IntDef_Oint_decl,type,
c_IntDef_Oint: $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Divides_Oop_Amod_decl,type,
c_Divides_Oop_Amod: $i > $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(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_IntDef_Oint @ A )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ) ) ) ).
thf(592,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(2163,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(829,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
thf(2612,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
thf(2306,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)],[664]) ).
thf(382,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
thf(1767,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(362,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).
thf(1729,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(450,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
thf(1899,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(420,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
thf(1840,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(334,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(1674,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1675,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[1674]) ).
thf(1676,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[1675]) ).
thf(2,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(1042,plain,
v_c != c_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1045,plain,
v_c != c_0,
inference(polarity_switch,[status(thm)],[1042]) ).
thf(1046,plain,
c_0 != v_c,
inference(lifteq,[status(thm)],[1045]) ).
thf(7625,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_c )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1046]) ).
thf(7626,plain,
! [A: $i] :
( ( A != v_c )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7625:[]]) ).
thf(8834,plain,
tc_nat @ ( v_c @ ( c_0 @ c_less ) ),
inference(simp,[status(thm)],[7626]) ).
thf(9031,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,8834]) ).
thf(9032,plain,
( ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9031:[bind(A,$thf( tc_nat ))]]) ).
thf(721,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(2413,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(2414,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[2413]) ).
thf(10046,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[9032,2414]) ).
thf(10047,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10046]) ).
thf(10066,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( tc_nat != A )
| ( c_0 != A )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10047]) ).
thf(10081,plain,
( ( tc_nat != c_0 )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10066]) ).
thf(792,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
thf(2544,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(242,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
thf(1503,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_27) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1106,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[1105]) ).
thf(6843,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(paramod_ordered,[status(thm)],[1503,1106]) ).
thf(6844,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(simp,[status(thm)],[6843]) ).
thf(6845,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1 ),
inference(pattern_uni,[status(thm)],[6844:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(677,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(2331,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).
thf(1295,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(611,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(2199,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(1040,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).
thf(3021,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(940,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
thf(2822,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(838,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
thf(2630,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(287,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).
thf(1586,plain,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
thf(1501,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(440,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
thf(1879,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_39) ).
thf(1337,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(899,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
thf(2744,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(974,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(2889,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)],[974]) ).
thf(411,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
thf(1823,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
thf(1190,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(680,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
thf(2336,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(562,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).
thf(2109,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(574,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
thf(2131,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(519,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
thf(2031,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(312,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
thf(1633,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(916,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(2777,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)],[916]) ).
thf(2778,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[2777]) ).
thf(273,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).
thf(1559,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(968,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(2876,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(659,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).
thf(2298,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(119,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
thf(1271,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1272,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[1271]) ).
thf(5324,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2298,1272]) ).
thf(5325,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5324]) ).
thf(5336,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B
!= ( c_0 @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5325]) ).
thf(5348,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[5336]) ).
thf(7558,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,5348]) ).
thf(7559,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[7558]) ).
thf(7560,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[7559:[bind(A,$thf( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) )),bind(B,$thf( C ))]]) ).
thf(8795,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[7560]) ).
thf(329,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
thf(1666,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1667,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[1666]) ).
thf(9794,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8795,1667]) ).
thf(9795,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9794]) ).
thf(9817,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9795]) ).
thf(9833,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9817]) ).
thf(921,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
thf(2787,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(425,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
thf(1850,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Otimes )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_3) ).
thf(1082,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Otimes )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Otimes )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(cnf,[status(esa)],[1082]) ).
thf(494,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
thf(1982,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(728,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
thf(2427,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(756,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_48) ).
thf(2480,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(480,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
thf(1956,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)],[480]) ).
thf(987,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(2915,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(3,negated_conjecture,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(1043,plain,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1047,plain,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(polarity_switch,[status(thm)],[1043]) ).
thf(5900,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2915,1047]) ).
thf(5901,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5900]) ).
thf(5913,plain,
! [A: $i] :
( ( tc_nat != t_a )
| ( A
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5901]) ).
thf(5923,plain,
( ( tc_nat != t_a )
| ( ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5913]) ).
thf(8075,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) )
| ( tc_nat != t_a )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,5923]) ).
thf(8076,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) )
| ( tc_nat != t_a )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8075]) ).
thf(8077,plain,
( ( tc_nat != t_a )
| ( tc_nat @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8076:[bind(A,$thf( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ))]]) ).
thf(272,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(1558,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_15) ).
thf(1129,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)],[44]) ).
thf(1130,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(cnf,[status(esa)],[1129]) ).
thf(11015,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[1558,1130]) ).
thf(11016,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11015]) ).
thf(11017,plain,
tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11016:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(11076,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11017,1130]) ).
thf(11077,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11076]) ).
thf(11078,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11077:[bind(A,$thf( tc_IntDef_Oint @ tc_set ))]]) ).
thf(11263,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11078,1130]) ).
thf(11264,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11263]) ).
thf(11265,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11264:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set ))]]) ).
thf(11380,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11265,1130]) ).
thf(11381,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11380]) ).
thf(11382,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11381:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set ))]]) ).
thf(12071,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11382,1130]) ).
thf(12072,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[12071]) ).
thf(12073,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[12072:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(1118,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1119,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(cnf,[status(esa)],[1118]) ).
thf(12460,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12073,1119]) ).
thf(12461,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[12460]) ).
thf(12462,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[12461:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(290,axiom,
tc_IntDef_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(1591,plain,
tc_IntDef_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(7548,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1591]) ).
thf(7549,plain,
( ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7548:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).
thf(1554,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_9) ).
thf(1109,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(cnf,[status(esa)],[1109]) ).
thf(634,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
thf(2250,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(983,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
thf(2908,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(1616,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)],[304]) ).
thf(1617,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(cnf,[status(esa)],[1616]) ).
thf(1618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[1617]) ).
thf(783,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(2527,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1036,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).
thf(3012,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(488,axiom,
tc_nat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(1971,plain,
tc_nat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(8080,plain,
! [A: $i] :
( ( A != v_x )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,5923]) ).
thf(8081,plain,
( ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ( tc_nat @ ( v_x @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8080:[bind(A,$thf( v_x ))]]) ).
thf(281,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(1574,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1575,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[1574]) ).
thf(15755,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_x @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ v_h @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(paramod_ordered,[status(thm)],[8081,1575]) ).
thf(15756,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_x @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ v_h @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[15755]) ).
thf(15763,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( v_x != c_0 )
| ( c_0 != A )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ v_h @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[15756]) ).
thf(15780,plain,
( ( v_x != c_0 )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ v_h @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[15763]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1041,plain,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(694,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).
thf(2363,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(1200,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(545,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
thf(2077,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(550,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(2086,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_4) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1062,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(cnf,[status(esa)],[1061]) ).
thf(3119,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Ominus )
!= ( B @ class_HOL_Ominus ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(paramod_ordered,[status(thm)],[2086,1062]) ).
thf(3120,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Ominus )
!= ( B @ class_HOL_Ominus ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(simp,[status(thm)],[3119]) ).
thf(3121,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(pattern_uni,[status(thm)],[3120:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(6135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Ominus )
!= ( C @ class_HOL_Ominus ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_HOL_Ominus ) ),
inference(paramod_ordered,[status(thm)],[3121,1062]) ).
thf(6136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Ominus )
!= ( C @ class_HOL_Ominus ) )
| ( C @ ( B @ tc_fun ) @ class_HOL_Ominus ) ),
inference(simp,[status(thm)],[6135]) ).
thf(6137,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(pattern_uni,[status(thm)],[6136:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6142,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(simp,[status(thm)],[6137]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
thf(1156,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)],[59]) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(cnf,[status(esa)],[1156]) ).
thf(1158,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(lifteq,[status(thm)],[1157]) ).
thf(773,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(2512,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_28) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(cnf,[status(esa)],[1074]) ).
thf(4374,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(paramod_ordered,[status(thm)],[1503,1075]) ).
thf(4375,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(simp,[status(thm)],[4374]) ).
thf(4376,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ),
inference(pattern_uni,[status(thm)],[4375:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(223,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).
thf(1467,plain,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Osemigroup__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_7) ).
thf(1059,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Osemigroup__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1060,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Osemigroup__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(cnf,[status(esa)],[1059]) ).
thf(3070,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add )
!= ( B @ class_OrderedGroup_Osemigroup__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(paramod_ordered,[status(thm)],[1467,1060]) ).
thf(3071,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add )
!= ( B @ class_OrderedGroup_Osemigroup__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(simp,[status(thm)],[3070]) ).
thf(3072,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ),
inference(pattern_uni,[status(thm)],[3071:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(851,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(2654,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(10995,plain,
! [A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[2654,1130]) ).
thf(10996,plain,
! [A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[10995]) ).
thf(10997,plain,
tc_nat @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[10996:[bind(A,$thf( tc_nat ))]]) ).
thf(11053,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[10997,1130]) ).
thf(11054,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11053]) ).
thf(11055,plain,
tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11054:[bind(A,$thf( tc_nat @ tc_set ))]]) ).
thf(11135,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11055,1130]) ).
thf(11136,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11135]) ).
thf(11137,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11136:[bind(A,$thf( tc_nat @ tc_set @ tc_set ))]]) ).
thf(11341,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11137,1130]) ).
thf(11342,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11341]) ).
thf(11343,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11342:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set ))]]) ).
thf(11856,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11343,1130]) ).
thf(11857,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11856]) ).
thf(11858,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[11857:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(12424,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11858,1130]) ).
thf(12425,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[12424]) ).
thf(12426,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[12425:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(2210,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)],[617]) ).
thf(566,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
thf(2117,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1001,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(2940,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)],[1001]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
thf(1406,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(11254,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11078,1119]) ).
thf(11255,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[11254]) ).
thf(11256,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[11255:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set ))]]) ).
thf(7516,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_OrderedGroup_Oab__group__add )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2544]) ).
thf(7517,plain,
( ( c_0 @ class_OrderedGroup_Oab__group__add )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7516:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(834,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
thf(2622,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_16) ).
thf(1068,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(932,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
thf(2808,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(846,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
thf(2644,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(764,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(2495,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(703,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
thf(2381,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(7640,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_OrderedGroup_Ocomm__monoid__mult )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2654]) ).
thf(7641,plain,
( ( c_0 @ class_OrderedGroup_Ocomm__monoid__mult )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7640:[bind(A,$thf( tc_nat ))]]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).
thf(1443,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(854,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
thf(2659,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(cnf,[status(esa)],[1068]) ).
thf(4766,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[2654,1069]) ).
thf(4767,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[4766]) ).
thf(4768,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[4767:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(9695,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4768,1119]) ).
thf(9696,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[9695]) ).
thf(9697,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[9696:[bind(A,$thf( C )),bind(B,$thf( tc_nat @ ( C @ tc_fun ) ))]]) ).
thf(9704,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[9697]) ).
thf(1006,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(2953,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)],[1006]) ).
thf(818,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
thf(2590,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).
thf(1401,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).
thf(1422,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1004,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).
thf(2947,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(472,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
thf(1939,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(633,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
thf(2248,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_29) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ) ),
inference(cnf,[status(esa)],[1063]) ).
thf(3096,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[1503,1064]) ).
thf(3097,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ) ),
inference(simp,[status(thm)],[3096]) ).
thf(3098,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ),
inference(pattern_uni,[status(thm)],[3097:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_19) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1073,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ) ),
inference(cnf,[status(esa)],[1072]) ).
thf(265,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
thf(1544,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(863,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(2676,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)],[863]) ).
thf(557,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(2099,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).
thf(1142,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(1269,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)],[118]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_4) ).
thf(1486,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_22) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ) ),
inference(cnf,[status(esa)],[1088]) ).
thf(5499,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ) ),
inference(paramod_ordered,[status(thm)],[1503,1089]) ).
thf(5500,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ) ),
inference(simp,[status(thm)],[5499]) ).
thf(5501,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ),
inference(pattern_uni,[status(thm)],[5500:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(300,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
thf(1608,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(3023,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1041,1047]) ).
thf(3024,plain,
! [A: $i] :
( ( t_a @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[3023]) ).
thf(3025,plain,
! [A: $i] :
( ( t_a != t_a )
| ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( t_a @ ( A @ v_h @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) ) ),
inference(simp,[status(thm)],[3024]) ).
thf(3026,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( t_a @ ( A @ v_h @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) ) ),
inference(simp,[status(thm)],[3025]) ).
thf(3030,plain,
! [A: $i] :
( ( t_a != t_a )
| ( ( t_a @ ( A @ v_f @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) ) )
| ( ( t_a @ ( v_c @ c_HOL_Oabs ) )
!= v_c )
| ( t_a != t_a )
| ( ( A @ v_h )
!= ( v_x @ v_h ) ) ),
inference(simp,[status(thm)],[3026]) ).
thf(3033,plain,
! [A: $i] :
( ( ( t_a @ ( A @ v_f @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) ) )
| ( ( t_a @ ( v_c @ c_HOL_Oabs ) )
!= v_c )
| ( ( A @ v_h )
!= ( v_x @ v_h ) ) ),
inference(simp,[status(thm)],[3030]) ).
thf(3034,plain,
! [A: $i] :
( ( ( t_a @ ( A @ v_f @ c_HOL_Oabs ) )
!= ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) ) )
| ( ( t_a @ ( v_c @ c_HOL_Oabs ) )
!= v_c )
| ( A != v_x ) ),
inference(simp,[status(thm)],[3033]) ).
thf(3037,plain,
( ( t_a @ ( v_c @ c_HOL_Oabs ) )
!= v_c ),
inference(simp,[status(thm)],[3034]) ).
thf(3482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( t_a @ ( v_c @ c_HOL_Oabs ) ) )
| ( D != v_c )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,3037]) ).
thf(3483,plain,
! [C: $i,B: $i,A: $i] :
( ( C != v_c )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3482:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_a @ ( v_c @ c_HOL_Oabs ) )),bind(D,$thf( D ))]]) ).
thf(4090,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( v_c @ c_in ) ) )
| ~ ( B @ ( A @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[3483]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
thf(1137,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(436,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
thf(1872,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(393,axiom,
tc_nat @ class_HOL_Otimes,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_11) ).
thf(1789,plain,
tc_nat @ class_HOL_Otimes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Otimes )
| ( A @ tc_set @ class_HOL_Otimes ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_6) ).
thf(1133,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Otimes )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1134,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Otimes )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(cnf,[status(esa)],[1133]) ).
thf(11538,plain,
! [A: $i] :
( ( ( tc_nat @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[1789,1134]) ).
thf(11539,plain,
! [A: $i] :
( ( ( tc_nat @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11538]) ).
thf(11540,plain,
tc_nat @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11539:[bind(A,$thf( tc_nat ))]]) ).
thf(11588,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11540,1134]) ).
thf(11589,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11588]) ).
thf(11590,plain,
tc_nat @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11589:[bind(A,$thf( tc_nat @ tc_set ))]]) ).
thf(11641,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11590,1134]) ).
thf(11642,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11641]) ).
thf(11643,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11642:[bind(A,$thf( tc_nat @ tc_set @ tc_set ))]]) ).
thf(11816,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11643,1134]) ).
thf(11817,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11816]) ).
thf(11818,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11817:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set ))]]) ).
thf(12156,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11818,1134]) ).
thf(12157,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[12156]) ).
thf(12158,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[12157:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).
thf(1327,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(525,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
thf(2042,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
thf(1507,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(810,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
thf(2575,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(239,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).
thf(1497,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1038,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
thf(3017,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(609,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
thf(2195,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(349,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
thf(1705,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_20) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).
thf(1426,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(9040,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_c @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8834,1667]) ).
thf(9041,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9040]) ).
thf(9057,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != v_c )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9041]) ).
thf(9063,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( v_c @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9057]) ).
thf(9118,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( v_c @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,9063]) ).
thf(9119,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( v_c @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9118]) ).
thf(9120,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[9119:[bind(A,$thf( tc_nat @ ( D @ ( v_c @ c_plus ) ) )),bind(B,$thf( D ))]]) ).
thf(9127,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[9120]) ).
thf(868,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(2686,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)],[868]) ).
thf(11012,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[4768,1130]) ).
thf(11013,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11012]) ).
thf(11014,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[11013:[bind(A,$thf( C )),bind(B,$thf( tc_nat @ ( C @ tc_fun ) ))]]) ).
thf(11029,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[11014]) ).
thf(139,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
thf(1310,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(897,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
thf(2740,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(989,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
thf(2918,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(365,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
thf(1735,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(11056,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[10997,1069]) ).
thf(11057,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11056]) ).
thf(11058,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[11057:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ tc_set ))]]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
thf(1163,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1164,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(cnf,[status(esa)],[1163]) ).
thf(669,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
thf(2316,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(121,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(1275,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(580,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
thf(2141,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(754,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).
thf(2476,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
thf(1260,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(497,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
thf(1988,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(745,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).
thf(2459,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(379,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
thf(1761,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(813,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
thf(2580,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(248,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(1513,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(7033,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1513,1667]) ).
thf(7034,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[7033]) ).
thf(7053,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[7034]) ).
thf(7068,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[7053]) ).
thf(479,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
thf(1954,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1034,axiom,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).
thf(3009,plain,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(5261,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3009,1272]) ).
thf(5262,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5261]) ).
thf(5274,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5262]) ).
thf(5285,plain,
! [A: $i] :
( ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[5274]) ).
thf(7940,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( c_1 @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,5285]) ).
thf(7941,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( c_1 @ ( B @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[7940]) ).
thf(7942,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[7941:[bind(A,$thf( tc_nat @ ( c_1 @ ( C @ c_plus ) ) )),bind(B,$thf( C ))]]) ).
thf(8929,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[7942]) ).
thf(9390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8929,1272]) ).
thf(9391,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9390]) ).
thf(9404,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9391]) ).
thf(9433,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9404]) ).
thf(532,axiom,
tc_IntDef_Oint @ class_HOL_Otimes,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
thf(2055,plain,
tc_IntDef_Oint @ class_HOL_Otimes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(4889,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[2055,1083]) ).
thf(4890,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[4889]) ).
thf(4891,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[4890:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(11541,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[4891,1134]) ).
thf(11542,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11541]) ).
thf(11543,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[11542:[bind(A,$thf( C )),bind(B,$thf( tc_IntDef_Oint @ ( C @ tc_fun ) ))]]) ).
thf(11549,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(simp,[status(thm)],[11543]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oplus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_2) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oplus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oplus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oplus ) ),
inference(cnf,[status(esa)],[1094]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
thf(1196,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(371,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
thf(1746,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(887,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(2723,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(470,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(1935,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(296,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
thf(1601,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(401,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
thf(1803,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(964,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(2869,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)],[964]) ).
thf(444,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_45) ).
thf(1887,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(620,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
thf(2216,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(11573,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11540,1083]) ).
thf(11574,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11573]) ).
thf(11575,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[11574:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ tc_set ))]]) ).
thf(13444,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11575,1134]) ).
thf(13445,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[13444]) ).
thf(13446,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[13445:[bind(A,$thf( C )),bind(B,$thf( tc_nat @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(13452,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(simp,[status(thm)],[13446]) ).
thf(540,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(2068,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)],[540]) ).
thf(2069,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(cnf,[status(esa)],[2068]) ).
thf(9042,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( v_c @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8834,2069]) ).
thf(9043,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( v_c @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9042]) ).
thf(9058,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( v_c != B )
| ( c_0 != A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9043]) ).
thf(9064,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ~ ( A @ tc_set @ ( c_0 @ ( v_c @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9058]) ).
thf(527,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
thf(2046,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(5976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != v_x )
| ( tc_nat != t_a )
| ( ( t_a @ ( C @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,5923]) ).
thf(5977,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != t_a )
| ( ( t_a @ ( C @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( v_x @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[5976:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( v_x ))]]) ).
thf(459,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_52) ).
thf(1914,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(762,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
thf(2491,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(1127,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(909,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
thf(2763,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(1022,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
thf(2985,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(624,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
thf(2227,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
thf(1576,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(321,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
thf(1650,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(463,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
thf(1921,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(972,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
thf(2884,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(2885,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(polarity_switch,[status(thm)],[2884]) ).
thf(2886,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(lifteq,[status(thm)],[2885]) ).
thf(164,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
thf(1359,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(3314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != c_0 )
| ( D != v_c )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1046]) ).
thf(3315,plain,
! [C: $i,B: $i,A: $i] :
( ( C != v_c )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( c_0 @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3314:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_0 ))]]) ).
thf(4030,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( v_c @ c_in ) ) )
| ~ ( B @ ( A @ ( c_0 @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[3315]) ).
thf(359,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
thf(1724,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(597,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_31) ).
thf(2173,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_31) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(cnf,[status(esa)],[1070]) ).
thf(4229,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(paramod_ordered,[status(thm)],[1503,1071]) ).
thf(4230,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(simp,[status(thm)],[4229]) ).
thf(4231,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ),
inference(pattern_uni,[status(thm)],[4230:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(6270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ) ),
inference(paramod_ordered,[status(thm)],[4231,1073]) ).
thf(6271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ) ),
inference(simp,[status(thm)],[6270]) ).
thf(6272,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ),
inference(pattern_uni,[status(thm)],[6271:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6306,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ),
inference(simp,[status(thm)],[6272]) ).
thf(168,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
thf(1366,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(713,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_15) ).
thf(2400,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(486,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
thf(1967,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(577,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).
thf(2136,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(251,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).
thf(1518,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(348,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).
thf(1703,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(785,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
thf(2531,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(716,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
thf(2405,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(307,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_30) ).
thf(1623,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(231,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
thf(1482,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
thf(1254,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_11) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
thf(1287,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(351,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
thf(1709,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_26) ).
thf(1080,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1081,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ) ),
inference(cnf,[status(esa)],[1080]) ).
thf(4741,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ) ),
inference(paramod_ordered,[status(thm)],[1503,1081]) ).
thf(4742,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ) ),
inference(simp,[status(thm)],[4741]) ).
thf(4743,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ),
inference(pattern_uni,[status(thm)],[4742:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
thf(1323,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)],[146]) ).
thf(866,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
thf(2682,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).
thf(1279,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(5259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3009,2069]) ).
thf(5260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5259]) ).
thf(5269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( c_1 != B )
| ( c_0 != A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5260]) ).
thf(5279,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ~ ( A @ tc_set @ ( c_0 @ ( c_1 @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5269]) ).
thf(675,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
thf(2328,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(988,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(2916,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(395,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).
thf(1792,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1430,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(894,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(2735,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(661,axiom,
tc_nat @ class_LOrder_Olorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(2301,plain,
tc_nat @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(7700,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_LOrder_Olorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2301]) ).
thf(7701,plain,
( ( c_0 @ class_LOrder_Olorder )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7700:[bind(A,$thf( tc_nat ))]]) ).
thf(874,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_43) ).
thf(2698,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
thf(1660,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)],[326]) ).
thf(4149,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[1558,1069]) ).
thf(4150,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[4149]) ).
thf(4151,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[4150:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(905,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
thf(2755,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(11138,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11055,1069]) ).
thf(11139,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11138]) ).
thf(11140,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[11139:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ tc_set @ tc_set ))]]) ).
thf(14334,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11140,1119]) ).
thf(14335,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[14334]) ).
thf(14336,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[14335:[bind(A,$thf( C )),bind(B,$thf( tc_nat @ tc_set @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(14351,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[14336]) ).
thf(737,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/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(2443,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)],[737]) ).
thf(2444,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(cnf,[status(esa)],[2443]) ).
thf(430,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
thf(1860,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
thf(1264,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(247,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
thf(1511,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(646,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).
thf(2274,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(604,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_27) ).
thf(2185,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(216,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
thf(1455,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(243,axiom,
tc_nat @ class_HOL_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_1) ).
thf(1504,plain,
tc_nat @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ozero )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_5) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ozero )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1087,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ozero )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ozero ) ),
inference(cnf,[status(esa)],[1086]) ).
thf(5180,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Ozero )
!= ( B @ class_HOL_Ozero ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Ozero ) ),
inference(paramod_ordered,[status(thm)],[1504,1087]) ).
thf(5181,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Ozero )
!= ( B @ class_HOL_Ozero ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ozero ) ),
inference(simp,[status(thm)],[5180]) ).
thf(5182,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Ozero ),
inference(pattern_uni,[status(thm)],[5181:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(3088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2444]) ).
thf(3089,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 ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3088]) ).
thf(760,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
thf(2488,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(416,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
thf(1832,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(978,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
thf(2897,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_10) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1091,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(cnf,[status(esa)],[1090]) ).
thf(5710,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(paramod_ordered,[status(thm)],[2544,1091]) ).
thf(5711,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(simp,[status(thm)],[5710]) ).
thf(5712,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__semigroup__add ),
inference(pattern_uni,[status(thm)],[5711:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(499,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
thf(1992,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(749,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
thf(2466,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(571,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
thf(2126,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(220,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
thf(1462,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(1131,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1132,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(cnf,[status(esa)],[1131]) ).
thf(6201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( C @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[4151,1069]) ).
thf(6202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( C @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[6201]) ).
thf(6203,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[6202:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6208,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[6203]) ).
thf(3028,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( t_a != t_a )
| ( ( A @ v_h )
!= ( v_x @ v_h ) ) ),
inference(simp,[status(thm)],[3026]) ).
thf(3031,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( ( A @ v_h )
!= ( v_x @ v_h ) ) ),
inference(simp,[status(thm)],[3028]) ).
thf(3040,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( A != v_x ) ),
inference(simp,[status(thm)],[3031]) ).
thf(3043,plain,
( ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) )
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) ) ),
inference(simp,[status(thm)],[3040]) ).
thf(808,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
thf(2571,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(5257,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3009,1667]) ).
thf(5258,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5257]) ).
thf(5276,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_1 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5258]) ).
thf(5287,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[5276]) ).
thf(8504,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( c_1 @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,5287]) ).
thf(8505,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( c_1 @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8504]) ).
thf(8506,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[8505:[bind(A,$thf( tc_nat @ ( D @ ( c_1 @ c_plus ) ) )),bind(B,$thf( D ))]]) ).
thf(8753,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[8506]) ).
thf(882,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__plus ) ) @ ( A @ ( B @ ( D @ c_SetsAndFunctions_Oelt__set__plus ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono_0) ).
thf(2713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__plus ) ) @ ( A @ ( B @ ( D @ c_SetsAndFunctions_Oelt__set__plus ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(175,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
thf(1379,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
thf(1147,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(1319,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(6279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Oring__1 ) ),
inference(paramod_ordered,[status(thm)],[4231,1064]) ).
thf(6280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Oring__1 ) ),
inference(simp,[status(thm)],[6279]) ).
thf(6281,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ),
inference(pattern_uni,[status(thm)],[6280:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6310,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring__1 ),
inference(simp,[status(thm)],[6281]) ).
thf(589,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
thf(2158,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(1773,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)],[385]) ).
thf(786,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
thf(2533,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(595,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_14) ).
thf(2169,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(715,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
thf(2403,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
thf(1514,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)],[249]) ).
thf(699,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).
thf(2373,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(801,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(2560,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(cnf,[status(esa)],[1200]) ).
thf(4618,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2560,1201]) ).
thf(4619,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[4618]) ).
thf(4620,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[4619:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(4622,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[4620]) ).
thf(158,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).
thf(1347,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(280,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
thf(1572,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1114,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[1113]) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) ) ),
inference(lifteq,[status(thm)],[1114]) ).
thf(841,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
thf(2635,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(778,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
thf(2520,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(7727,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_OrderedGroup_Ocancel__semigroup__add )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2520]) ).
thf(7728,plain,
( ( c_0 @ class_OrderedGroup_Ocancel__semigroup__add )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7727:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
thf(1931,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(278,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
thf(1568,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(3059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( B @ ( C @ c_lessequals ) ) ) )
| ~ $true
| ~ ( D @ tc_set @ ( C @ ( B @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1041,2069]) ).
thf(3060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( B @ ( C @ c_lessequals ) ) ) )
| ~ ( D @ tc_set @ ( C @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[3059]) ).
thf(3061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_set )
!= t_a )
| ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= B )
| ( ( t_a @ ( A @ v_h @ c_HOL_Oabs ) )
!= C )
| ~ ( D @ tc_set @ ( C @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[3060]) ).
thf(3062,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= t_a )
| ~ ( B @ tc_set @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[3061]) ).
thf(7041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( t_a @ ( B @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( B @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) ) )
| ( ( C @ tc_set )
!= t_a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1513,3062]) ).
thf(7042,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( t_a @ ( B @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( B @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) ) )
| ( ( C @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[7041]) ).
thf(7047,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( ( A @ c_Suc )
!= ( t_a @ ( B @ v_h @ c_HOL_Oabs ) ) )
| ( ( t_a @ ( t_a @ ( B @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= c_0 )
| ( ( C @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[7042]) ).
thf(1037,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(3014,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)],[1037]) ).
thf(891,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
thf(2730,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(366,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_14) ).
thf(1737,plain,
tc_nat @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(3078,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Osemigroup__add )
!= ( B @ class_OrderedGroup_Osemigroup__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(paramod_ordered,[status(thm)],[1737,1060]) ).
thf(3079,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Osemigroup__add )
!= ( B @ class_OrderedGroup_Osemigroup__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(simp,[status(thm)],[3078]) ).
thf(3080,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ),
inference(pattern_uni,[status(thm)],[3079:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(6091,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add )
!= ( C @ class_OrderedGroup_Osemigroup__add ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(paramod_ordered,[status(thm)],[3080,1060]) ).
thf(6092,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add )
!= ( C @ class_OrderedGroup_Osemigroup__add ) )
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(simp,[status(thm)],[6091]) ).
thf(6093,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ),
inference(pattern_uni,[status(thm)],[6092:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_nat @ ( D @ tc_fun ) ))]]) ).
thf(6098,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ),
inference(simp,[status(thm)],[6093]) ).
thf(316,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(1641,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(407,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(1815,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
thf(1494,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1024,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(2989,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)],[1024]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(1362,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)],[166]) ).
thf(484,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
thf(1963,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1099,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[1098]) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) ) ),
inference(lifteq,[status(thm)],[1099]) ).
thf(7508,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_OrderedGroup_Osemigroup__mult )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1586]) ).
thf(7509,plain,
( ( c_0 @ class_OrderedGroup_Osemigroup__mult )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7508:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
thf(1232,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(13713,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12426,1119]) ).
thf(13714,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[13713]) ).
thf(13715,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[13714:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(507,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
thf(2007,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1005,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
thf(2950,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(457,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_6) ).
thf(1911,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(849,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
thf(2650,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(492,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
thf(1978,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(7676,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Ring__and__Field_Oordered__semiring__strict )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1462]) ).
thf(7677,plain,
( ( c_0 @ class_Ring__and__Field_Oordered__semiring__strict )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7676:[bind(A,$thf( tc_nat ))]]) ).
thf(56,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
thf(1151,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_8) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1051,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(cnf,[status(esa)],[1050]) ).
thf(512,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
thf(2017,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(831,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
thf(2616,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
thf(1465,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_50) ).
thf(1302,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(328,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
thf(1664,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(925,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(2794,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(673,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
thf(2324,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(517,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_32) ).
thf(2027,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(560,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
thf(2105,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(3074,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2778]) ).
thf(3075,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3074]) ).
thf(405,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_60) ).
thf(1811,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(7257,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_IntDef_Oint @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2512,4622]) ).
thf(7258,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_IntDef_Oint @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[7257]) ).
thf(7286,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_IntDef_Oint )
| ( ( A @ c_Suc )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[7258]) ).
thf(7300,plain,
! [A: $i] :
( ( tc_nat != tc_IntDef_Oint )
| ( ( A @ c_Suc )
!= A ) ),
inference(simp,[status(thm)],[7286]) ).
thf(172,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
thf(1373,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(976,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(2893,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)],[976]) ).
thf(625,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
thf(2229,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(2230,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(cnf,[status(esa)],[2229]) ).
thf(2231,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(lifteq,[status(thm)],[2230]) ).
thf(2232,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ),
inference(detectInverse,[status(thm)],[2231]) ).
thf(2233,plain,
! [A: $i] :
( ( A @ c_Suc @ sk2 )
= A ),
inference(cnf,[status(esa)],[2232]) ).
thf(7104,plain,
! [A: $i] :
( ( A @ c_Suc @ sk2 )
= A ),
inference(lifteq,[status(thm)],[2233]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
thf(1418,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(741,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
thf(2451,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(627,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_14) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(970,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(2880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
thf(1135,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1136,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(cnf,[status(esa)],[1135]) ).
thf(429,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
thf(1858,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)],[429]) ).
thf(432,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
thf(1864,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(3346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ( D
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) ) )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,3043]) ).
thf(3347,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3346:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) )),bind(D,$thf( D ))]]) ).
thf(4050,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_in ) ) )
| ~ ( B @ ( A @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[3347]) ).
thf(569,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
thf(2122,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(655,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
thf(2291,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(177,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
thf(1383,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(636,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
thf(2254,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(335,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).
thf(1677,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(521,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).
thf(2034,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(482,axiom,
tc_nat @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(1960,plain,
tc_nat @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(798,axiom,
tc_IntDef_Oint @ class_HOL_Oplus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).
thf(2555,plain,
tc_IntDef_Oint @ class_HOL_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_20) ).
thf(1283,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(543,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
thf(2073,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(696,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
thf(2367,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
thf(1377,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
thf(1447,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(160,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
thf(1351,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)],[160]) ).
thf(12409,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11858,1119]) ).
thf(12410,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[12409]) ).
thf(12411,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[12410:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(504,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
thf(2002,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(253,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_17) ).
thf(1521,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(614,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_13) ).
thf(2205,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(276,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
thf(1564,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_25) ).
thf(1111,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1112,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(cnf,[status(esa)],[1111]) ).
thf(7411,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(paramod_ordered,[status(thm)],[1503,1112]) ).
thf(7412,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(simp,[status(thm)],[7411]) ).
thf(7413,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Oaxclass__0__neq__1 ),
inference(pattern_uni,[status(thm)],[7412:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(771,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
thf(2508,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(66,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(1169,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(936,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(2815,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(5733,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2815,1201]) ).
thf(5734,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[5733]) ).
thf(5735,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[5734:[bind(A,$thf( D )),bind(B,$thf( D @ tc_set ))]]) ).
thf(5738,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[5735]) ).
thf(3318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( E @ c_Suc ) )
| ( D != c_0 )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,2886]) ).
thf(3319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != c_0 )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( D @ c_Suc @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3318:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( F @ c_Suc )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(4033,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( c_0 @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_Suc @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[3319]) ).
thf(832,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
thf(2618,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(650,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(2281,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)],[650]) ).
thf(960,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(2861,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(780,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
thf(2523,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(397,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
thf(1796,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(698,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
thf(2371,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)],[698]) ).
thf(1019,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(2979,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)],[1019]) ).
thf(183,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
thf(1394,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(913,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
thf(2772,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(630,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
thf(2242,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(157,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_49) ).
thf(1345,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(559,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( D @ c_plus ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono4_0) ).
thf(2103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( D @ c_plus ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(902,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
thf(2750,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(189,axiom,
tc_nat @ class_HOL_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
thf(1405,plain,
tc_nat @ class_HOL_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(474,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
thf(1943,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(930,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(2804,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1011,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(2965,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Osemigroup__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_13) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Osemigroup__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1104,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Osemigroup__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ) ),
inference(cnf,[status(esa)],[1103]) ).
thf(345,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
thf(1697,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
thf(1242,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(816,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
thf(2586,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
thf(2011,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
thf(1206,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)],[85]) ).
thf(984,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
thf(2910,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(342,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
thf(1691,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(206,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
thf(1438,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(847,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
thf(2646,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).
thf(1306,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(505,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_16) ).
thf(2004,plain,
tc_nat @ class_OrderedGroup_Osemigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(6682,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Osemigroup__mult )
!= ( B @ class_OrderedGroup_Osemigroup__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ) ),
inference(paramod_ordered,[status(thm)],[2004,1104]) ).
thf(6683,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Osemigroup__mult )
!= ( B @ class_OrderedGroup_Osemigroup__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ) ),
inference(simp,[status(thm)],[6682]) ).
thf(6684,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ),
inference(pattern_uni,[status(thm)],[6683:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
thf(1152,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1153,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(cnf,[status(esa)],[1152]) ).
thf(10998,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[4151,1130]) ).
thf(10999,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[10998]) ).
thf(11000,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[10999:[bind(A,$thf( C )),bind(B,$thf( tc_IntDef_Oint @ ( C @ tc_fun ) ))]]) ).
thf(11035,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[11000]) ).
thf(13038,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11035,1130]) ).
thf(13039,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[13038]) ).
thf(13040,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[13039:[bind(A,$thf( D )),bind(B,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) @ tc_set ))]]) ).
thf(13051,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[13040]) ).
thf(844,axiom,
tc_nat @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(2641,plain,
tc_nat @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(991,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
thf(2922,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(11523,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[2055,1134]) ).
thf(11524,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11523]) ).
thf(11525,plain,
tc_IntDef_Oint @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11524:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(11553,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11525,1083]) ).
thf(11554,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11553]) ).
thf(11555,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[11554:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint @ tc_set ))]]) ).
thf(3458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != t_a )
| ~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( C @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1047]) ).
thf(3459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( C @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( t_a @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3458:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_a ))]]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
thf(1470,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(554,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
thf(2093,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(390,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
thf(1783,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(895,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
thf(2737,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_30) ).
thf(1096,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(cnf,[status(esa)],[1096]) ).
thf(6303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(paramod_ordered,[status(thm)],[4231,1097]) ).
thf(6304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(simp,[status(thm)],[6303]) ).
thf(6305,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ),
inference(pattern_uni,[status(thm)],[6304:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6307,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ),
inference(simp,[status(thm)],[6305]) ).
thf(658,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
thf(2296,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(548,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
thf(2083,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1066,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[1065]) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) ) ),
inference(lifteq,[status(thm)],[1066]) ).
thf(765,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).
thf(2496,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(923,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
thf(2790,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(434,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
thf(1868,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(536,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
thf(2061,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(503,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
thf(2000,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_17) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_15) ).
thf(1223,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(746,axiom,
tc_nat @ class_HOL_Oplus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_10) ).
thf(2461,plain,
tc_nat @ class_HOL_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(6077,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Oplus )
!= ( B @ class_HOL_Oplus ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Oplus ) ),
inference(paramod_ordered,[status(thm)],[2461,1095]) ).
thf(6078,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Oplus )
!= ( B @ class_HOL_Oplus ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oplus ) ),
inference(simp,[status(thm)],[6077]) ).
thf(6079,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Oplus ),
inference(pattern_uni,[status(thm)],[6078:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(821,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
thf(2596,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)],[821]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
thf(1122,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1123,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(cnf,[status(esa)],[1122]) ).
thf(1014,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
thf(2969,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(999,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
thf(2937,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(826,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
thf(2606,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)],[826]) ).
thf(736,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).
thf(2441,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(7729,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2730]) ).
thf(7730,plain,
( ( c_0 @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7729:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(878,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
thf(2705,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(641,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).
thf(2264,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(719,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
thf(2409,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(179,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(1387,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(358,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(1723,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(893,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
thf(2733,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(156,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
thf(1343,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(790,axiom,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(2541,plain,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(648,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_12) ).
thf(2277,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(162,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_28) ).
thf(1355,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(284,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
thf(1580,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_13) ).
thf(1570,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)],[279]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_14) ).
thf(1174,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(575,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
thf(2133,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_24) ).
thf(1217,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(583,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
thf(2147,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(11202,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( tc_nat != t_a ) ),
inference(paramod_ordered,[status(thm)],[8077,1272]) ).
thf(11203,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) ) )
| ( tc_nat != t_a ) ),
inference(simp,[status(thm)],[11202]) ).
thf(11212,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( tc_nat != t_a ) ),
inference(simp,[status(thm)],[11203]) ).
thf(11223,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( A @ c_plus ) ) )
!= c_0 )
| ( tc_nat != t_a ) ),
inference(simp,[status(thm)],[11212]) ).
thf(374,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
thf(1751,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(14754,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13051,1119]) ).
thf(14755,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[14754]) ).
thf(14756,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[14755:[bind(A,$thf( E )),bind(B,$thf( tc_IntDef_Oint @ ( E @ tc_fun ) @ tc_set @ tc_set ))]]) ).
thf(14772,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[14756]) ).
thf(305,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
thf(1619,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
thf(1370,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(711,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
thf(2396,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(11369,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11265,1119]) ).
thf(11370,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[11369]) ).
thf(11371,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[11370:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set ))]]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
thf(1238,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(511,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
thf(2015,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(9044,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_c @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8834,1272]) ).
thf(9045,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9044]) ).
thf(9052,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != v_c )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9045]) ).
thf(9070,plain,
! [A: $i] :
( ( tc_nat @ ( v_c @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9052]) ).
thf(9152,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( ( c_0 @ ( v_c @ ( B @ c_plus ) ) )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,9070]) ).
thf(9153,plain,
! [A: $i] :
( ( ( c_0 @ ( v_c @ ( A @ c_plus ) ) )
!= c_0 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9152:[bind(A,$thf( tc_nat ))]]) ).
thf(9158,plain,
! [A: $i] :
( ( ( c_0 @ ( v_c @ ( A @ c_plus ) ) )
!= c_0 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9153]) ).
thf(442,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
thf(1883,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(274,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
thf(1560,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1008,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).
thf(2958,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(11568,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11525,1134]) ).
thf(11569,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11568]) ).
thf(11570,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11569:[bind(A,$thf( tc_IntDef_Oint @ tc_set ))]]) ).
thf(5970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != tc_nat )
| ( D != t_a )
| ( ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,5923]) ).
thf(5971,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( tc_nat @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[5970:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( tc_nat ))]]) ).
thf(5983,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( t_a @ c_in ) ) )
| ~ ( B @ ( A @ ( tc_nat @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[5971]) ).
thf(462,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
thf(1920,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(731,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
thf(2433,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(804,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).
thf(2565,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
thf(1178,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(600,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
thf(2179,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_21) ).
thf(1159,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(cnf,[status(esa)],[1078]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
thf(1281,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(182,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
thf(1392,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
thf(1291,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(738,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
thf(2445,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)],[738]) ).
thf(4293,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ) ),
inference(paramod_ordered,[status(thm)],[1503,1073]) ).
thf(4294,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ) ),
inference(simp,[status(thm)],[4293]) ).
thf(4295,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0 ),
inference(pattern_uni,[status(thm)],[4294:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(748,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
thf(2464,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oone )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_6) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oone )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oone )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oone ) ),
inference(cnf,[status(esa)],[1092]) ).
thf(5877,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Oone )
!= ( B @ class_HOL_Oone ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Oone ) ),
inference(paramod_ordered,[status(thm)],[1405,1093]) ).
thf(5878,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Oone )
!= ( B @ class_HOL_Oone ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oone ) ),
inference(simp,[status(thm)],[5877]) ).
thf(5879,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Oone ),
inference(pattern_uni,[status(thm)],[5878:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(837,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
thf(2628,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(860,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
thf(2670,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(678,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
thf(2332,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(942,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
thf(2826,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)],[942]) ).
thf(939,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
thf(2820,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(966,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
thf(2872,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)],[966]) ).
thf(478,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
thf(1951,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(340,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
thf(1687,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
thf(1457,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(409,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
thf(1819,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(418,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
thf(1836,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(1787,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)],[392]) ).
thf(602,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
thf(2181,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
thf(1210,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(324,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).
thf(1656,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(3048,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(paramod_ordered,[status(thm)],[1394,1051]) ).
thf(3049,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(simp,[status(thm)],[3048]) ).
thf(3050,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ),
inference(pattern_uni,[status(thm)],[3049:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(685,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
thf(2345,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)],[685]) ).
thf(1128,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(cnf,[status(esa)],[1127]) ).
thf(794,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(2547,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(684,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
thf(2344,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(368,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
thf(1740,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(456,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(1910,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(7607,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Ring__and__Field_Osemiring__0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2575]) ).
thf(7608,plain,
( ( c_0 @ class_Ring__and__Field_Osemiring__0 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7607:[bind(A,$thf( tc_nat ))]]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono_0) ).
thf(1360,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)],[165]) ).
thf(291,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(1592,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)],[291]) ).
thf(775,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
thf(2515,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(701,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
thf(2377,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(977,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(2895,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(950,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
thf(2841,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(428,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).
thf(1856,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(872,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
thf(2694,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(7202,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(paramod_ordered,[status(thm)],[2344,1110]) ).
thf(7203,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(simp,[status(thm)],[7202]) ).
thf(7204,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ),
inference(pattern_uni,[status(thm)],[7203:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(376,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
thf(1755,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(643,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
thf(2268,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(1030,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
thf(3001,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
thf(1397,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).
thf(1234,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(766,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
thf(2498,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1143,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(cnf,[status(esa)],[1142]) ).
thf(565,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
thf(2115,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(260,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_54) ).
thf(1534,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(396,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
thf(1794,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1016,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(2973,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)],[1016]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
thf(1120,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1121,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(cnf,[status(esa)],[1120]) ).
thf(692,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
thf(2359,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(173,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
thf(1375,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
thf(1227,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(880,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
thf(2709,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(871,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
thf(2692,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(288,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_57) ).
thf(1587,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(332,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
thf(1672,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(263,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
thf(1540,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(3746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != c_0 )
| ~ ( tc_nat @ ( D @ ( E @ c_less ) ) )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1575]) ).
thf(3747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_less ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( c_0 @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3746:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_0 ))]]) ).
thf(3963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_less ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( c_0 @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[3747]) ).
thf(439,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(1878,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(889,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
thf(2726,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(4892,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[1789,1083]) ).
thf(4893,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[4892]) ).
thf(4894,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[4893:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(11535,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[4894,1134]) ).
thf(11536,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11535]) ).
thf(11537,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[11536:[bind(A,$thf( C )),bind(B,$thf( tc_nat @ ( C @ tc_fun ) ))]]) ).
thf(11548,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(simp,[status(thm)],[11537]) ).
thf(13155,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11548,1134]) ).
thf(13156,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[13155]) ).
thf(13157,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[13156:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ ( D @ tc_fun ) @ tc_set ))]]) ).
thf(13163,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_HOL_Otimes ),
inference(simp,[status(thm)],[13157]) ).
thf(1138,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(cnf,[status(esa)],[1137]) ).
thf(356,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
thf(1719,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(11126,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11055,1119]) ).
thf(11127,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[11126]) ).
thf(11128,plain,
tc_nat @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[11127:[bind(A,$thf( tc_nat @ tc_set @ tc_set ))]]) ).
thf(959,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
thf(2858,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(788,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
thf(2537,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(11843,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11343,1119]) ).
thf(11844,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[11843]) ).
thf(11845,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[11844:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(2638,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)],[843]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1160,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(cnf,[status(esa)],[1159]) ).
thf(802,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
thf(2561,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(286,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
thf(1584,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(471,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(1937,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(858,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/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro2_0) ).
thf(2666,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)],[858]) ).
thf(918,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).
thf(2781,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(927,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
thf(2798,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(338,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
thf(1683,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(515,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
thf(2023,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(944,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_8) ).
thf(2830,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
thf(1182,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(724,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_16) ).
thf(2419,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
thf(1424,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(667,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
thf(2312,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1035,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
thf(3010,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(743,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(2455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
thf(1414,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(531,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
thf(2053,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(629,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
thf(2240,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(421,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
thf(1842,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
thf(1214,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(687,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
thf(2349,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(523,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
thf(2038,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(211,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
thf(1446,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(796,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).
thf(2551,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(549,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(2085,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(445,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
thf(1889,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
thf(1644,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).
thf(1612,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(752,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__intro2_0) ).
thf(2472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetsAndFunctions_Oelt__set__plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(7522,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_OrderedGroup_Oab__semigroup__mult )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2331]) ).
thf(7523,plain,
( ( c_0 @ class_OrderedGroup_Oab__semigroup__mult )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7522:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
thf(1154,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1155,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(cnf,[status(esa)],[1154]) ).
thf(370,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
thf(1744,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(12846,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11029,1130]) ).
thf(12847,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[12846]) ).
thf(12848,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[12847:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ ( D @ tc_fun ) @ tc_set ))]]) ).
thf(12859,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[12848]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).
thf(1297,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(495,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
thf(1984,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(437,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
thf(1874,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(354,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
thf(1715,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1032,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
thf(3005,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)],[1032]) ).
thf(645,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
thf(2272,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(412,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).
thf(1825,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(652,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
thf(2285,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(769,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
thf(2504,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(996,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(2932,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)],[996]) ).
thf(13409,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11555,1134]) ).
thf(13410,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[13409]) ).
thf(13411,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[13410:[bind(A,$thf( C )),bind(B,$thf( tc_IntDef_Oint @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(13415,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes ),
inference(simp,[status(thm)],[13411]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
thf(1149,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1150,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(cnf,[status(esa)],[1149]) ).
thf(229,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
thf(1478,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(214,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
thf(1451,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(663,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
thf(2304,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(258,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
thf(1530,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(947,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
thf(2836,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(952,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(2845,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)],[952]) ).
thf(822,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
thf(2598,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(116,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
thf(1266,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(586,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
thf(2153,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(706,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
thf(2387,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(98,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
thf(1231,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
thf(1668,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(490,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
thf(1974,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(269,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
thf(1552,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(955,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(2851,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)],[955]) ).
thf(690,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
thf(2355,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
thf(1192,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(805,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).
thf(2566,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(399,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
thf(1799,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(7788,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_LOrder_Omeet__semilorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1960]) ).
thf(7789,plain,
( ( c_0 @ class_LOrder_Omeet__semilorder )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7788:[bind(A,$thf( tc_nat ))]]) ).
thf(476,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
thf(1947,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)],[476]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
thf(1852,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(935,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
thf(2813,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(910,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
thf(2766,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(530,axiom,
tc_IntDef_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(2052,plain,
tc_IntDef_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(757,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).
thf(2482,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
thf(1599,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono3_0) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_SetsAndFunctions_Oelt__set__plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(579,axiom,
tc_IntDef_Oint @ class_HOL_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
thf(2140,plain,
tc_IntDef_Oint @ class_HOL_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(5320,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2298,1667]) ).
thf(5321,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5320]) ).
thf(5338,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A
!= ( c_0 @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5321]) ).
thf(5350,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[5338]) ).
thf(8108,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,5350]) ).
thf(8109,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8108]) ).
thf(8110,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[8109:[bind(A,$thf( tc_nat @ ( D @ ( c_0 @ c_Suc @ c_plus ) ) )),bind(B,$thf( D ))]]) ).
thf(8980,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[8110]) ).
thf(3081,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Ominus )
!= ( B @ class_HOL_Ominus ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(paramod_ordered,[status(thm)],[1169,1062]) ).
thf(3082,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_HOL_Ominus )
!= ( B @ class_HOL_Ominus ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(simp,[status(thm)],[3081]) ).
thf(3083,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(pattern_uni,[status(thm)],[3082:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(378,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
thf(1759,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(309,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
thf(1627,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)],[309]) ).
thf(255,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
thf(1525,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(151,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(1333,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)],[151]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
thf(1434,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(993,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/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono3_0) ).
thf(2926,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)],[993]) ).
thf(388,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
thf(1779,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(616,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).
thf(2208,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(344,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
thf(1695,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1010,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
thf(2963,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(621,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Osemigroup__add )
| ( A @ tc_set @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_9) ).
thf(2221,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Osemigroup__add )
| ( A @ tc_set @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(6282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(paramod_ordered,[status(thm)],[4231,1075]) ).
thf(6283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(simp,[status(thm)],[6282]) ).
thf(6284,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ),
inference(pattern_uni,[status(thm)],[6283:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6311,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1__cancel ),
inference(simp,[status(thm)],[6284]) ).
thf(856,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
thf(2662,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)],[856]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(1202,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(613,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
thf(2203,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(876,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
thf(2702,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(908,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(2761,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)],[908]) ).
thf(4194,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_in ) ) )
!= ( B @ ( A @ ( v_c @ c_in ) ) ) )
| ~ ( B @ ( A @ ( v_c @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(eqfactor_ordered,[status(thm)],[4090]) ).
thf(4195,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_in ) ) )
!= ( B @ ( A @ ( v_c @ c_in ) ) ) )
| ~ ( B @ ( A @ ( v_c @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[4194]) ).
thf(534,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
thf(2057,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(423,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
thf(1846,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1053,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[1052]) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) ) ),
inference(lifteq,[status(thm)],[1053]) ).
thf(901,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).
thf(2748,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
thf(1170,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)],[67]) ).
thf(718,axiom,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(2408,plain,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(552,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
thf(2089,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(448,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
thf(1895,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
thf(1167,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(606,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
thf(2189,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1027,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/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono2_0) ).
thf(2995,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)],[1027]) ).
thf(681,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(2338,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(501,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
thf(1996,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(726,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(2423,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)],[726]) ).
thf(784,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/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro_0) ).
thf(2529,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)],[784]) ).
thf(568,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
thf(2121,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(3490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != v_c )
| ( ( t_a @ ( C @ c_HOL_Oabs ) )
!= v_c )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,3037]) ).
thf(3491,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( C @ c_HOL_Oabs ) )
!= v_c )
| ~ ( B @ ( A @ ( v_c @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3490:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( v_c ))]]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
thf(1273,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(824,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
thf(2602,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
thf(1595,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(7784,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2291]) ).
thf(7785,plain,
( ( c_0 @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7784:[bind(A,$thf( tc_nat ))]]) ).
thf(311,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_51) ).
thf(1631,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(639,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(2260,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(123,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
thf(1278,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(454,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
thf(1906,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(998,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(2936,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(320,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
thf(1648,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(361,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
thf(1727,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)],[361]) ).
thf(6291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ) ),
inference(paramod_ordered,[status(thm)],[4231,1081]) ).
thf(6292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ) ),
inference(simp,[status(thm)],[6291]) ).
thf(6293,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ),
inference(pattern_uni,[status(thm)],[6292:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6314,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__1 ),
inference(simp,[status(thm)],[6293]) ).
thf(53,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(1146,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(656,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
thf(2292,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(708,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
thf(2391,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)],[708]) ).
thf(981,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(2904,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(799,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
thf(2556,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(520,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
thf(2033,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
thf(2149,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(884,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(2717,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
thf(1219,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(372,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
thf(1747,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(11330,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11137,1119]) ).
thf(11331,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[11330]) ).
thf(11332,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[11331:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set ))]]) ).
thf(267,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).
thf(1548,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(466,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
thf(1927,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(5880,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Oone )
!= ( B @ class_HOL_Oone ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Oone ) ),
inference(paramod_ordered,[status(thm)],[2140,1093]) ).
thf(5881,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Oone )
!= ( B @ class_HOL_Oone ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oone ) ),
inference(simp,[status(thm)],[5880]) ).
thf(5882,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Oone ),
inference(pattern_uni,[status(thm)],[5881:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(5978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != t_a )
| ( tc_nat != t_a )
| ( ( C @ ( v_x @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,5923]) ).
thf(5979,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != t_a )
| ( ( C @ ( v_x @ v_h @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( t_a @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[5978:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_a ))]]) ).
thf(460,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).
thf(1916,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(1020,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(2981,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
thf(1388,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(485,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).
thf(1965,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(252,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
thf(1520,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(41,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
thf(1124,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(528,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_3) ).
thf(2048,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1000,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(2938,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(7638,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Ring__and__Field_Opordered__cancel__semiring )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1359]) ).
thf(7639,plain,
( ( c_0 @ class_Ring__and__Field_Opordered__cancel__semiring )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7638:[bind(A,$thf( tc_nat ))]]) ).
thf(623,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).
thf(2225,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(922,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(2789,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(6285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(paramod_ordered,[status(thm)],[4231,1071]) ).
thf(6286,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(simp,[status(thm)],[6285]) ).
thf(6287,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ),
inference(pattern_uni,[status(thm)],[6286:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6312,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 ),
inference(simp,[status(thm)],[6287]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).
thf(1125,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(781,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(2525,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(853,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_36) ).
thf(2657,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(954,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(2849,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(709,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(2393,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
thf(1652,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(467,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
thf(1929,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(9692,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4151,1119]) ).
thf(9693,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[9692]) ).
thf(9694,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[9693:[bind(A,$thf( C )),bind(B,$thf( tc_IntDef_Oint @ ( C @ tc_fun ) ))]]) ).
thf(9706,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[9694]) ).
thf(862,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
thf(2674,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)],[862]) ).
thf(806,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
thf(2568,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(4603,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(paramod_ordered,[status(thm)],[1503,1079]) ).
thf(4604,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(simp,[status(thm)],[4603]) ).
thf(4605,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ),
inference(pattern_uni,[status(thm)],[4604:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(931,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
thf(2806,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)],[931]) ).
thf(1025,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
thf(2991,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)],[1025]) ).
thf(5972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) )
| ( tc_nat != t_a )
| ( C != c_0 )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,5923]) ).
thf(5973,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != t_a )
| ( C != c_0 )
| ~ ( B @ ( A @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[5972:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ))]]) ).
thf(5984,plain,
! [B: $i,A: $i] :
( ( tc_nat != t_a )
| ~ ( B @ ( A @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_in ) ) )
| ~ ( B @ ( A @ ( c_0 @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[5973]) ).
thf(188,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
thf(1403,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(347,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
thf(1701,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(712,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
thf(2398,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(5265,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) ) )
| ( ( B @ tc_set )
!= t_a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3009,3062]) ).
thf(5266,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) ) )
| ( ( B @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[5265]) ).
thf(5271,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( ( t_a @ ( A @ v_h @ c_HOL_Oabs ) )
!= c_1 )
| ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= c_0 )
| ( ( B @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[5266]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).
thf(1256,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
thf(1488,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
thf(1428,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(7199,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(paramod_ordered,[status(thm)],[1394,1110]) ).
thf(7200,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(simp,[status(thm)],[7199]) ).
thf(7201,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__add ),
inference(pattern_uni,[status(thm)],[7200:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).
thf(1707,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_21) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(cnf,[status(esa)],[1101]) ).
thf(6530,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(paramod_ordered,[status(thm)],[1503,1102]) ).
thf(6531,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(simp,[status(thm)],[6530]) ).
thf(6532,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring__0__cancel ),
inference(pattern_uni,[status(thm)],[6531:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(896,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(2738,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(13077,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11058,1130]) ).
thf(13078,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[13077]) ).
thf(13079,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[13078:[bind(A,$thf( C )),bind(B,$thf( tc_nat @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(13093,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[13079]) ).
thf(727,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
thf(2425,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).
thf(1258,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(7037,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1513,1272]) ).
thf(7038,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[7037]) ).
thf(7049,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[7038]) ).
thf(7062,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[7049]) ).
thf(809,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(2573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).
thf(1139,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(608,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
thf(2193,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_24) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1085,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ) ),
inference(cnf,[status(esa)],[1084]) ).
thf(5037,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ) ),
inference(paramod_ordered,[status(thm)],[1503,1085]) ).
thf(5038,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ) ),
inference(simp,[status(thm)],[5037]) ).
thf(5039,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ),
inference(pattern_uni,[status(thm)],[5038:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(518,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
thf(2029,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)],[518]) ).
thf(674,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
thf(2326,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(975,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(2891,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)],[975]) ).
thf(665,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
thf(2308,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(3076,plain,
! [C: $i,B: $i,A: $i] :
( ( C != C )
| ( ( C @ tc_set @ ( B @ c_uminus ) )
!= B )
| ( A != A )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3074]) ).
thf(3077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ c_uminus ) )
!= B )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3076]) ).
thf(10055,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[9032,1272]) ).
thf(10056,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10055]) ).
thf(10068,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10056]) ).
thf(10083,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10068]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_15) ).
thf(1312,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Ocomm__monoid__mult )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(313,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
thf(1635,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(364,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
thf(1733,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(1058,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ) ),
inference(cnf,[status(esa)],[1057]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_12) ).
thf(1107,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(907,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(2759,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)],[907]) ).
thf(904,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
thf(2753,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(744,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
thf(2457,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(449,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
thf(1897,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(3090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != C )
| ( ( C @ tc_set @ ( B @ ( D @ c_minus ) ) )
!= B )
| ( A != A )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3088]) ).
thf(3091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( D @ c_minus ) ) )
!= B )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3090]) ).
thf(753,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
thf(2474,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(772,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
thf(2510,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(79,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(1194,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(779,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
thf(2521,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)],[779]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).
thf(1116,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1117,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(cnf,[status(esa)],[1116]) ).
thf(914,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
thf(2774,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(264,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
thf(1542,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(949,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
thf(2839,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(546,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).
thf(2079,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(693,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
thf(2361,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(6019,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add )
!= ( C @ class_OrderedGroup_Osemigroup__add ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(paramod_ordered,[status(thm)],[3072,1060]) ).
thf(6020,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add )
!= ( C @ class_OrderedGroup_Osemigroup__add ) )
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ) ),
inference(simp,[status(thm)],[6019]) ).
thf(6021,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ),
inference(pattern_uni,[status(thm)],[6020:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6024,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__add ),
inference(simp,[status(thm)],[6021]) ).
thf(886,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
thf(2721,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(567,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
thf(2119,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(7782,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_OrderedGroup_Ocancel__semigroup__add )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1151]) ).
thf(7783,plain,
( ( c_0 @ class_OrderedGroup_Ocancel__semigroup__add )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7782:[bind(A,$thf( tc_nat ))]]) ).
thf(191,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).
thf(1408,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(6273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(paramod_ordered,[status(thm)],[4231,1079]) ).
thf(6274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(simp,[status(thm)],[6273]) ).
thf(6275,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ),
inference(pattern_uni,[status(thm)],[6274:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6308,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0 ),
inference(simp,[status(thm)],[6275]) ).
thf(755,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
thf(2478,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(585,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
thf(2151,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(845,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
thf(2642,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(619,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(2214,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(704,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( E @ c_plus ) ) @ ( A @ tc_set @ ( B @ ( D @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono2_0) ).
thf(2383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( C @ ( E @ c_plus ) ) @ ( A @ tc_set @ ( B @ ( D @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(835,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
thf(2624,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(722,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
thf(2415,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)],[722]) ).
thf(9148,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( v_c @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,9070]) ).
thf(9149,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( v_c @ ( B @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9148]) ).
thf(9150,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[9149:[bind(A,$thf( tc_nat @ ( v_c @ ( C @ c_plus ) ) )),bind(B,$thf( C ))]]) ).
thf(9165,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[9150]) ).
thf(9569,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9165,1667]) ).
thf(9570,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9569]) ).
thf(9592,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( v_c @ ( A @ c_plus ) ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9570]) ).
thf(9614,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9592]) ).
thf(763,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
thf(2493,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(1023,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(2987,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(982,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(2906,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_23) ).
thf(1048,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
thf(1349,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)],[159]) ).
thf(9293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8753,1667]) ).
thf(9294,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9293]) ).
thf(9307,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9294]) ).
thf(9322,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9307]) ).
thf(556,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
thf(2097,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
thf(1589,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(469,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
thf(1933,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
thf(2246,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)],[632]) ).
thf(236,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
thf(1492,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(297,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
thf(1603,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_18) ).
thf(1076,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(cnf,[status(esa)],[1076]) ).
thf(6300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(paramod_ordered,[status(thm)],[4231,1077]) ).
thf(6301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(simp,[status(thm)],[6300]) ).
thf(6302,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ),
inference(pattern_uni,[status(thm)],[6301:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6321,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ),
inference(simp,[status(thm)],[6302]) ).
thf(660,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).
thf(2299,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(11266,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11078,1069]) ).
thf(11267,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11266]) ).
thf(11268,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[11267:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint @ tc_set @ tc_set ))]]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
thf(1144,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(384,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
thf(1771,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(8078,plain,
! [A: $i] :
( ( A
!= ( v_x @ v_h ) )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ c_HOL_Oabs ) )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,5923]) ).
thf(8079,plain,
( ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ c_HOL_Oabs ) )
!= c_0 )
| ( tc_nat @ ( v_x @ v_h @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8078:[bind(A,$thf( v_x @ v_h ))]]) ).
thf(15366,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_x @ v_h @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(paramod_ordered,[status(thm)],[8079,2414]) ).
thf(15367,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_x @ v_h @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[15366]) ).
thf(15385,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( v_x @ v_h )
!= A )
| ( c_0 != A )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[15367]) ).
thf(15401,plain,
( ( ( v_x @ v_h )
!= c_0 )
| ( tc_nat != t_a )
| ( ( t_a @ ( c_0 @ c_HOL_Oabs ) )
!= c_0 ) ),
inference(simp,[status(thm)],[15385]) ).
thf(1003,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(2945,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)],[1003]) ).
thf(5322,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2298,2069]) ).
thf(5323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5322]) ).
thf(5334,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( ( c_0 @ c_Suc )
!= B )
| ( c_0 != A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5323]) ).
thf(5346,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ~ ( A @ tc_set @ ( c_0 @ ( c_0 @ c_Suc @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5334]) ).
thf(400,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
thf(1801,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(958,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( A @ ( D @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
thf(2856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( A @ ( D @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(929,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
thf(2802,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(610,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
thf(2197,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(487,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
thf(1969,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(9122,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( ( c_0 @ ( B @ ( v_c @ c_plus ) ) )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,9063]) ).
thf(9123,plain,
! [A: $i] :
( ( ( c_0 @ ( A @ ( v_c @ c_plus ) ) )
!= c_0 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9122:[bind(A,$thf( tc_nat ))]]) ).
thf(9129,plain,
! [A: $i] :
( ( ( c_0 @ ( A @ ( v_c @ c_plus ) ) )
!= c_0 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9123]) ).
thf(898,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
thf(2742,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1049,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Ring__and__Field_Ocomm__ring__1 )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(cnf,[status(esa)],[1048]) ).
thf(3053,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(paramod_ordered,[status(thm)],[1503,1049]) ).
thf(3054,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(simp,[status(thm)],[3053]) ).
thf(3055,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ),
inference(pattern_uni,[status(thm)],[3054:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(12475,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[12073,1130]) ).
thf(12476,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[12475]) ).
thf(12477,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult,
inference(pattern_uni,[status(thm)],[12476:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(62,axiom,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
thf(1162,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(906,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
thf(2757,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(920,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
thf(2785,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(601,axiom,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(2180,plain,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(941,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
thf(2824,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(516,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
thf(2025,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(934,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(2812,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(839,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(2632,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(7698,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Ring__and__Field_Osemiring__1 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2635]) ).
thf(7699,plain,
( ( c_0 @ class_Ring__and__Field_Osemiring__1 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7698:[bind(A,$thf( tc_nat ))]]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
thf(1339,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(828,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
thf(2610,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(668,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_56) ).
thf(2314,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(573,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
thf(2129,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(7263,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2512,2414]) ).
thf(7264,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[7263]) ).
thf(7281,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[7264]) ).
thf(7292,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(simp,[status(thm)],[7281]) ).
thf(563,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_29) ).
thf(2111,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(410,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
thf(1821,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(363,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).
thf(1731,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(11614,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11570,1134]) ).
thf(11615,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11614]) ).
thf(11616,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11615:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set ))]]) ).
thf(11782,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11616,1134]) ).
thf(11783,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11782]) ).
thf(11784,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[11783:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set ))]]) ).
thf(12115,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11784,1134]) ).
thf(12116,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[12115]) ).
thf(12117,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[12116:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(12526,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[12117,1134]) ).
thf(12527,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[12526]) ).
thf(12528,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[12527:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(431,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Oplus )
| ( A @ tc_set @ class_HOL_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_5) ).
thf(1862,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Oplus )
| ( A @ tc_set @ class_HOL_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(7550,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1971]) ).
thf(7551,plain,
( ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7550:[bind(A,$thf( tc_nat ))]]) ).
thf(419,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
thf(1838,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
thf(1325,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(6297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ) ),
inference(paramod_ordered,[status(thm)],[4231,1085]) ).
thf(6298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ) ),
inference(simp,[status(thm)],[6297]) ).
thf(6299,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ),
inference(pattern_uni,[status(thm)],[6298:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6319,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring ),
inference(simp,[status(thm)],[6299]) ).
thf(967,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(2874,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)],[967]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
thf(1556,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(791,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
thf(2542,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(219,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
thf(1460,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(654,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
thf(2289,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(635,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(2252,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)],[635]) ).
thf(857,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
thf(2664,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
thf(1293,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(797,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
thf(2553,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(994,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(2928,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
thf(1381,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(7276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( C @ tc_set @ ( t_a @ ( B @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( B @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) ) )
| ( ( C @ tc_set )
!= t_a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2512,3062]) ).
thf(7277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( C @ tc_set @ ( t_a @ ( B @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( B @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) ) )
| ( ( C @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[7276]) ).
thf(7284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( ( A @ c_Suc )
!= ( t_a @ ( B @ v_h @ c_HOL_Oabs ) ) )
| ( A
!= ( t_a @ ( t_a @ ( B @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) ) )
| ( ( C @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[7277]) ).
thf(7297,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_Suc )
!= ( t_a @ ( A @ v_h @ c_HOL_Oabs ) ) )
| ( ( B @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[7284]) ).
thf(9297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8753,1272]) ).
thf(9298,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9297]) ).
thf(9312,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9298]) ).
thf(9327,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( c_1 @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9312]) ).
thf(812,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
thf(2578,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(695,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
thf(2365,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(227,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
thf(1474,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(4,negated_conjecture,
t_a @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(1044,plain,
t_a @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
thf(1176,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(840,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
thf(2633,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(238,axiom,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(1496,plain,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(615,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
thf(2207,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(402,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
thf(1805,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(912,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
thf(2770,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(544,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
thf(2075,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).
thf(1198,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(9573,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9165,1272]) ).
thf(9574,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9573]) ).
thf(9589,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( v_c @ ( A @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9574]) ).
thf(9610,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( v_c @ ( A @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9589]) ).
thf(735,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
thf(2439,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(888,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(2725,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(346,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
thf(1699,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(714,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
thf(2401,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(292,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
thf(1594,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(618,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
thf(2212,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(596,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
thf(2171,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(833,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
thf(2620,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)],[833]) ).
thf(210,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(1445,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
thf(1528,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(538,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
thf(2064,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(697,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).
thf(2369,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(631,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
thf(2244,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(903,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
thf(2752,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(386,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
thf(1775,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(819,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
thf(2592,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(787,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
thf(2535,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(558,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
thf(2101,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)],[558]) ).
thf(360,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
thf(1726,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(167,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_10) ).
thf(1364,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1013,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
thf(2967,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)],[1013]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(1250,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)],[108]) ).
thf(1029,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
thf(2999,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(588,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
thf(2156,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(963,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
thf(2867,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)],[963]) ).
thf(770,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
thf(2506,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
thf(1562,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(12058,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11382,1119]) ).
thf(12059,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[12058]) ).
thf(12060,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[12059:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(404,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
thf(1809,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_53) ).
thf(1304,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
thf(1208,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(670,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).
thf(2318,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(850,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
thf(2652,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(969,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
thf(2878,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)],[969]) ).
thf(6074,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Oplus )
!= ( B @ class_HOL_Oplus ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Oplus ) ),
inference(paramod_ordered,[status(thm)],[2555,1095]) ).
thf(6075,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Oplus )
!= ( B @ class_HOL_Oplus ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oplus ) ),
inference(simp,[status(thm)],[6074]) ).
thf(6076,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Oplus ),
inference(pattern_uni,[status(thm)],[6075:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(481,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
thf(1958,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(979,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(2899,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(814,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
thf(2582,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(506,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
thf(2005,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(937,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
thf(2816,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(986,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
thf(2914,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(327,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(1662,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(830,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Osemigroup__mult )
| ( A @ tc_set @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_10) ).
thf(2614,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Osemigroup__mult )
| ( A @ tc_set @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
thf(1165,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1166,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(cnf,[status(esa)],[1165]) ).
thf(561,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_25) ).
thf(2107,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(453,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
thf(1905,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(197,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
thf(1420,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(570,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).
thf(2124,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(626,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
thf(2234,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(740,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
thf(2449,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(246,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
thf(1509,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(14382,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11268,1119]) ).
thf(14383,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[14382]) ).
thf(14384,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[14383:[bind(A,$thf( C )),bind(B,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(14406,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[14384]) ).
thf(498,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
thf(1990,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(867,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_41) ).
thf(2684,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(6504,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( C @ class_HOL_Otimes ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[4891,1083]) ).
thf(6505,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Otimes )
!= ( C @ class_HOL_Otimes ) )
| ( C @ ( B @ tc_fun ) @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[6504]) ).
thf(6506,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[6505:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6517,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(simp,[status(thm)],[6506]) ).
thf(3454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ) )
| ~ ( t_a @ ( C @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1047]) ).
thf(3455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3454:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_a @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) ))]]) ).
thf(226,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(1472,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1145,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(cnf,[status(esa)],[1144]) ).
thf(637,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
thf(2256,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1002,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
thf(2942,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(774,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
thf(2513,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(883,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
thf(2715,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)],[883]) ).
thf(483,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
thf(1961,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(855,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
thf(2661,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
thf(1225,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(13029,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11035,1119]) ).
thf(13030,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[13029]) ).
thf(13031,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[13030:[bind(A,$thf( D )),bind(B,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) @ tc_set ))]]) ).
thf(13047,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[13031]) ).
thf(971,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
thf(2882,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
thf(1516,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(961,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(2863,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1018,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
thf(2977,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(700,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
thf(2375,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
thf(1566,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(581,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
thf(2143,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(298,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(1605,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(817,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
thf(2588,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(473,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
thf(1941,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(1252,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)],[109]) ).
thf(864,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
thf(2678,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(777,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).
thf(2518,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
thf(1368,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)],[169]) ).
thf(598,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(2175,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(375,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oidom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_2) ).
thf(1753,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oidom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(3056,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ) ),
inference(paramod_ordered,[status(thm)],[1503,1058]) ).
thf(3057,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ) ),
inference(simp,[status(thm)],[3056]) ).
thf(3058,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ),
inference(pattern_uni,[status(thm)],[3057:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(717,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(2407,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
thf(1267,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
thf(1484,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(590,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).
thf(2160,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(807,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
thf(2569,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(13946,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12477,1119]) ).
thf(13947,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[13946]) ).
thf(13948,plain,
tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[13947:[bind(A,$thf( tc_IntDef_Oint @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(394,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
thf(1790,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(990,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
thf(2920,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(13068,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11058,1119]) ).
thf(13069,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[13068]) ).
thf(13070,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[13069:[bind(A,$thf( C )),bind(B,$thf( tc_nat @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(13089,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[13070]) ).
thf(391,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
thf(1785,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
thf(1262,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(1679,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(526,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
thf(2044,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(750,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
thf(2468,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(352,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
thf(1711,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1039,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
thf(3019,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(240,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
thf(1499,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(203,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
thf(1432,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(593,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
thf(2165,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(406,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
thf(1813,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
thf(1637,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(869,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
thf(2688,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_40) ).
thf(1188,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(875,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
thf(2700,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
thf(1186,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(729,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
thf(2429,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(647,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
thf(2276,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(493,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
thf(1980,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(572,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(2128,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__group__add ) ),
inference(cnf,[status(esa)],[1107]) ).
thf(6964,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__group__add ) ),
inference(paramod_ordered,[status(thm)],[2544,1108]) ).
thf(6965,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__group__add ) ),
inference(simp,[status(thm)],[6964]) ).
thf(6966,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__group__add ),
inference(pattern_uni,[status(thm)],[6965:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_7) ).
thf(1317,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(415,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
thf(1830,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)],[415]) ).
thf(380,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(1763,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)],[380]) ).
thf(11620,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11590,1083]) ).
thf(11621,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11620]) ).
thf(11622,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[11621:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ tc_set @ tc_set ))]]) ).
thf(451,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).
thf(1901,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(11079,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11017,1069]) ).
thf(11080,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[11079]) ).
thf(11081,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[11080:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint @ tc_set ))]]) ).
thf(6288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring ) ),
inference(paramod_ordered,[status(thm)],[4231,1058]) ).
thf(6289,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Osemiring ) ),
inference(simp,[status(thm)],[6288]) ).
thf(6290,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ),
inference(pattern_uni,[status(thm)],[6289:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6313,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Osemiring ),
inference(simp,[status(thm)],[6290]) ).
thf(325,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
thf(1658,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(672,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
thf(2322,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(262,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
thf(1538,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(759,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
thf(2486,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(793,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).
thf(2545,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
thf(1285,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(367,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
thf(1738,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(533,axiom,
tc_IntDef_Oint @ class_HOL_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).
thf(2056,plain,
tc_IntDef_Oint @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(9478,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9127,1667]) ).
thf(9479,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9478]) ).
thf(9494,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( v_c @ c_plus ) ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9479]) ).
thf(9505,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9494]) ).
thf(3492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != t_a )
| ( ( C @ ( v_c @ c_HOL_Oabs ) )
!= v_c )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,3037]) ).
thf(3493,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( v_c @ c_HOL_Oabs ) )
!= v_c )
| ~ ( B @ ( A @ ( t_a @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3492:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_a ))]]) ).
thf(702,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
thf(2379,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(373,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
thf(1749,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(171,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
thf(1372,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(815,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).
thf(2584,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
thf(1240,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(720,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
thf(2411,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(767,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
thf(2500,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(948,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
thf(2838,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(800,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(2558,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(564,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
thf(2113,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(50,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
thf(1141,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(4132,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ ( c_0 @ c_in ) ) )
!= ( B @ ( A @ ( v_c @ c_in ) ) ) )
| ~ ( B @ ( A @ ( v_c @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(eqfactor_ordered,[status(thm)],[4030]) ).
thf(4133,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_0 @ c_in ) ) )
!= ( B @ ( A @ ( v_c @ c_in ) ) ) )
| ~ ( B @ ( A @ ( v_c @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[4132]) ).
thf(261,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
thf(1536,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_59) ).
thf(1221,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1017,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).
thf(2975,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(161,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_35) ).
thf(1353,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(649,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
thf(2279,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(691,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(2357,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(951,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
thf(2843,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(582,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).
thf(2145,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(489,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
thf(1972,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(671,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_9) ).
thf(2320,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(881,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
thf(2711,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(4429,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(paramod_ordered,[status(thm)],[1503,1077]) ).
thf(4430,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(simp,[status(thm)],[4429]) ).
thf(4431,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring ),
inference(pattern_uni,[status(thm)],[4430:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(1140,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(cnf,[status(esa)],[1139]) ).
thf(7611,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1746]) ).
thf(7612,plain,
( ( c_0 @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7611:[bind(A,$thf( tc_nat ))]]) ).
thf(331,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_44) ).
thf(1670,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(398,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(1797,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(890,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
thf(2728,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(355,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
thf(1717,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(441,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).
thf(1881,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1033,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(3007,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(642,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
thf(2266,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(962,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
thf(2865,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)],[962]) ).
thf(732,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
thf(2435,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(14706,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12859,1119]) ).
thf(14707,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[14706]) ).
thf(14708,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[14707:[bind(A,$thf( E )),bind(B,$thf( tc_nat @ ( E @ tc_fun ) @ tc_set @ tc_set ))]]) ).
thf(14732,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[14708]) ).
thf(339,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(1685,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(873,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
thf(2696,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1126,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(cnf,[status(esa)],[1125]) ).
thf(510,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
thf(2013,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(2217,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(cnf,[status(esa)],[2216]) ).
thf(2218,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(lifteq,[status(thm)],[2217]) ).
thf(2219,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_IntDef_Oint @ A )
= B ),
inference(detectInverse,[status(thm)],[2218]) ).
thf(2220,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ sk1 )
= A ),
inference(cnf,[status(esa)],[2219]) ).
thf(7089,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ sk1 )
= A ),
inference(lifteq,[status(thm)],[2220]) ).
thf(992,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
thf(2924,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(836,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
thf(2626,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(461,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_33) ).
thf(1918,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(3456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( v_x @ v_f ) )
| ~ ( t_a @ ( t_a @ ( t_a @ ( C @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1047]) ).
thf(3457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( t_a @ ( C @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( v_x @ v_f @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3456:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( v_x @ v_f ))]]) ).
thf(142,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
thf(1316,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(5177,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Ozero )
!= ( B @ class_HOL_Ozero ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Ozero ) ),
inference(paramod_ordered,[status(thm)],[2056,1087]) ).
thf(5178,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_HOL_Ozero )
!= ( B @ class_HOL_Ozero ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ozero ) ),
inference(simp,[status(thm)],[5177]) ).
thf(5179,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_HOL_Ozero ),
inference(pattern_uni,[status(thm)],[5178:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(218,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(1459,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(938,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_set @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_7) ).
thf(2818,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_set @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
thf(1180,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(477,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
thf(1949,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(965,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/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono4_0) ).
thf(2870,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)],[965]) ).
thf(943,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
thf(2828,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(408,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
thf(1817,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1009,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(2960,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)],[1009]) ).
thf(145,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
thf(1321,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(417,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
thf(1834,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(458,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
thf(1913,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(666,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).
thf(2310,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(422,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
thf(1844,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(686,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
thf(2347,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(323,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
thf(1654,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(193,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).
thf(1412,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(389,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
thf(1781,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(90,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
thf(1216,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(6672,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult )
!= ( B @ class_OrderedGroup_Osemigroup__mult ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ) ),
inference(paramod_ordered,[status(thm)],[1586,1104]) ).
thf(6673,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult )
!= ( B @ class_OrderedGroup_Osemigroup__mult ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ) ),
inference(simp,[status(thm)],[6672]) ).
thf(6674,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Osemigroup__mult ),
inference(pattern_uni,[status(thm)],[6673:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(1028,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
thf(2997,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(761,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(2490,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(605,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
thf(2187,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(181,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_12) ).
thf(1390,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(683,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(2342,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
thf(1289,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(215,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
thf(1453,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(5328,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) ) )
| ( ( B @ tc_set )
!= t_a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2298,3062]) ).
thf(5329,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( t_a @ ( A @ v_h @ c_HOL_Oabs ) @ ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) ) )
| ( ( B @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[5328]) ).
thf(5332,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( ( t_a @ ( A @ v_h @ c_HOL_Oabs ) )
!= ( c_0 @ c_Suc ) )
| ( ( t_a @ ( t_a @ ( A @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) )
!= c_0 )
| ( ( B @ tc_set )
!= t_a ) ),
inference(simp,[status(thm)],[5329]) ).
thf(433,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
thf(1866,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(542,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
thf(2071,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(915,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
thf(2775,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
thf(1807,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(4308,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(paramod_ordered,[status(thm)],[2344,1051]) ).
thf(4309,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_OrderedGroup_Ocomm__monoid__add )
!= ( B @ class_OrderedGroup_Ocomm__monoid__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(simp,[status(thm)],[4308]) ).
thf(4310,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__add ),
inference(pattern_uni,[status(thm)],[4309:[bind(A,$thf( A )),bind(B,$thf( tc_nat ))]]) ).
thf(924,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
thf(2792,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(502,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
thf(1998,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(3592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != t_a )
| ( C @ class_Ring__and__Field_Oordered__idom )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1044]) ).
thf(3593,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ class_Ring__and__Field_Oordered__idom )
| ~ ( B @ ( A @ ( t_a @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3592:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_a ))]]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_38) ).
thf(1276,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(879,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
thf(2707,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(594,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
thf(2167,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(1341,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(956,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
thf(2853,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(13107,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11081,1119]) ).
thf(13108,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[13107]) ).
thf(13109,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[13108:[bind(A,$thf( C )),bind(B,$thf( tc_IntDef_Oint @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(13129,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[13109]) ).
thf(1015,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
thf(2971,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)],[1015]) ).
thf(427,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
thf(1854,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(782,axiom,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(2526,plain,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(710,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).
thf(2394,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
thf(1646,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(178,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
thf(1385,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(820,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
thf(2594,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(357,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
thf(1721,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)],[357]) ).
thf(651,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
thf(2283,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(707,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
thf(2389,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
thf(1476,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(957,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
thf(2855,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).
thf(1639,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(452,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
thf(1903,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(576,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(2135,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)],[576]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
thf(1629,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(827,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
thf(2608,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(730,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(2431,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)],[730]) ).
thf(1031,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
thf(3003,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
thf(1244,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(9798,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8795,1272]) ).
thf(9799,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9798]) ).
thf(9810,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9799]) ).
thf(9824,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9810]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
thf(1523,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(997,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(2934,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(640,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).
thf(2262,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(739,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
thf(2447,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(508,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
thf(2009,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1007,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
thf(2956,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(926,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).
thf(2796,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(985,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
thf(2912,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)],[985]) ).
thf(9482,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9127,1272]) ).
thf(9483,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9482]) ).
thf(9499,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( v_c @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9483]) ).
thf(9510,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( v_c @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9499]) ).
thf(747,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).
thf(2462,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_5) ).
thf(1308,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(980,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
thf(2902,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(208,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(1442,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(341,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
thf(1689,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(547,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
thf(2081,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(848,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
thf(2648,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(387,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
thf(1777,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(207,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_18) ).
thf(1440,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(676,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
thf(2330,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(811,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
thf(2576,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(539,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).
thf(2066,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(591,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(2162,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(865,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Oone )
| ( A @ tc_set @ class_HOL_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_8) ).
thf(2680,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Oone )
| ( A @ tc_set @ class_HOL_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
thf(2183,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
thf(1212,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(555,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
thf(2095,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(11069,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11017,1119]) ).
thf(11070,plain,
! [A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[11069]) ).
thf(11071,plain,
tc_IntDef_Oint @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[11070:[bind(A,$thf( tc_IntDef_Oint @ tc_set ))]]) ).
thf(522,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_37) ).
thf(2036,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(447,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
thf(1893,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(657,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
thf(2294,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)],[657]) ).
thf(500,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
thf(1994,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(6496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( C @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[4768,1069]) ).
thf(6497,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( C @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( C @ ( B @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[6496]) ).
thf(6498,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[6497:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_nat @ ( D @ tc_fun ) ))]]) ).
thf(6499,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[6498]) ).
thf(917,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
thf(2779,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)],[917]) ).
thf(513,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
thf(2019,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(61,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(1161,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(303,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
thf(1614,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(725,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
thf(2421,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(653,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
thf(2287,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(317,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
thf(1642,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)],[317]) ).
thf(283,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(1578,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(587,axiom,
tc_IntDef_Oint @ class_LOrder_Olorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(2155,plain,
tc_IntDef_Oint @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_42) ).
thf(1229,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(13116,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ~ $true
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(paramod_ordered,[status(thm)],[11081,1130]) ).
thf(13117,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(simp,[status(thm)],[13116]) ).
thf(13118,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(pattern_uni,[status(thm)],[13117:[bind(A,$thf( C )),bind(B,$thf( tc_IntDef_Oint @ tc_set @ ( C @ tc_fun ) ))]]) ).
thf(13133,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ),
inference(simp,[status(thm)],[13118]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
thf(1546,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(825,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
thf(2604,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)],[825]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
thf(1876,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(377,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
thf(1757,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
thf(1908,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)],[455]) ).
thf(995,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(2930,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(638,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
thf(2258,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(662,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
thf(2302,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(776,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(2517,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(5723,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_HOL_Ominus )
!= ( C @ class_HOL_Ominus ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_HOL_Ominus ) ),
inference(paramod_ordered,[status(thm)],[2085,1062]) ).
thf(5724,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_HOL_Ominus )
!= ( C @ class_HOL_Ominus ) )
| ( C @ ( B @ tc_fun ) @ class_HOL_Ominus ) ),
inference(simp,[status(thm)],[5723]) ).
thf(5725,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(pattern_uni,[status(thm)],[5724:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_set ))]]) ).
thf(5728,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(simp,[status(thm)],[5725]) ).
thf(9033,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( tc_nat @ ( v_c @ ( A @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,8834]) ).
thf(9034,plain,
! [A: $i] :
( ( tc_nat @ ( v_c @ ( A @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9033:[]]) ).
thf(705,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).
thf(2385,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(7633,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_OrderedGroup_Oab__semigroup__add )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,2400]) ).
thf(7634,plain,
( ( c_0 @ class_OrderedGroup_Oab__semigroup__add )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7633:[bind(A,$thf( tc_nat ))]]) ).
thf(1021,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
thf(2983,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(885,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
thf(2719,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
thf(1395,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(308,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
thf(1625,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(496,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
thf(1986,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(256,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(1527,plain,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1148,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(cnf,[status(esa)],[1147]) ).
thf(333,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
thf(1673,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
thf(1248,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)],[107]) ).
thf(529,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(2050,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(911,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
thf(2768,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
thf(1480,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(842,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
thf(2636,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(205,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
thf(1436,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(928,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).
thf(2800,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(679,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
thf(2334,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(6107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Ominus )
!= ( C @ class_HOL_Ominus ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_HOL_Ominus ) ),
inference(paramod_ordered,[status(thm)],[3083,1062]) ).
thf(6108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ class_HOL_Ominus )
!= ( C @ class_HOL_Ominus ) )
| ( C @ ( B @ tc_fun ) @ class_HOL_Ominus ) ),
inference(simp,[status(thm)],[6107]) ).
thf(6109,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(pattern_uni,[status(thm)],[6108:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_nat @ ( D @ tc_fun ) ))]]) ).
thf(6114,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_HOL_Ominus ),
inference(simp,[status(thm)],[6109]) ).
thf(11198,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( tc_nat != t_a ) ),
inference(paramod_ordered,[status(thm)],[8077,1667]) ).
thf(11199,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) ) )
| ( tc_nat != t_a ) ),
inference(simp,[status(thm)],[11198]) ).
thf(11217,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A
!= ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( tc_nat != t_a ) ),
inference(simp,[status(thm)],[11199]) ).
thf(11231,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_plus ) ) )
!= c_0 )
| ( tc_nat != t_a ) ),
inference(simp,[status(thm)],[11217]) ).
thf(6256,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(paramod_ordered,[status(thm)],[1503,1097]) ).
thf(6257,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( B @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( B @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(simp,[status(thm)],[6256]) ).
thf(6258,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__1__cancel ),
inference(pattern_uni,[status(thm)],[6257:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(553,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
thf(2091,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(446,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
thf(1891,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(622,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_19) ).
thf(2223,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(524,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
thf(2040,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(13374,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11549,1134]) ).
thf(13375,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[13374]) ).
thf(13376,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[13375:[bind(A,$thf( D )),bind(B,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) @ tc_set ))]]) ).
thf(13377,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ tc_set @ tc_set @ class_HOL_Otimes ),
inference(simp,[status(thm)],[13376]) ).
thf(919,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
thf(2783,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(612,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
thf(2201,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_OrderedGroup_Oab__group__add )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(cnf,[status(esa)],[1055]) ).
thf(4563,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(paramod_ordered,[status(thm)],[2544,1056]) ).
thf(4564,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add )
!= ( B @ class_OrderedGroup_Oab__group__add ) )
| ( B @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(simp,[status(thm)],[4563]) ).
thf(4565,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_OrderedGroup_Ocancel__ab__semigroup__add ),
inference(pattern_uni,[status(thm)],[4564:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint ))]]) ).
thf(11593,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ~ $true
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[11570,1083]) ).
thf(11594,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( B @ class_HOL_Otimes ) )
| ( B @ ( A @ tc_fun ) @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[11593]) ).
thf(11595,plain,
! [A: $i] : ( tc_IntDef_Oint @ tc_set @ tc_set @ ( A @ tc_fun ) @ class_HOL_Otimes ),
inference(pattern_uni,[status(thm)],[11594:[bind(A,$thf( A )),bind(B,$thf( tc_IntDef_Oint @ tc_set @ tc_set ))]]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
thf(1314,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(900,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
thf(2746,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(12732,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ~ $true
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(paramod_ordered,[status(thm)],[12158,1134]) ).
thf(12733,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes )
!= ( A @ class_HOL_Otimes ) )
| ( A @ tc_set @ class_HOL_Otimes ) ),
inference(simp,[status(thm)],[12732]) ).
thf(12734,plain,
tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set @ class_HOL_Otimes,
inference(pattern_uni,[status(thm)],[12733:[bind(A,$thf( tc_nat @ tc_set @ tc_set @ tc_set @ tc_set @ tc_set ))]]) ).
thf(152,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
thf(1335,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(343,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
thf(1693,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(541,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
thf(2070,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(877,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(2704,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
thf(1172,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)],[68]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(1410,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(723,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).
thf(2417,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(14802,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13093,1119]) ).
thf(14803,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[14802]) ).
thf(14804,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[14803:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ tc_set @ ( D @ tc_fun ) @ tc_set ))]]) ).
thf(14828,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[14804]) ).
thf(682,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_26) ).
thf(2340,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(859,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
thf(2668,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(9386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8929,1667]) ).
thf(9387,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9386]) ).
thf(9402,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9387]) ).
thf(9431,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( c_1 @ ( A @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9402]) ).
thf(514,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
thf(2021,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(6276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Oring ) ),
inference(paramod_ordered,[status(thm)],[4231,1089]) ).
thf(6277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Oring ) ),
inference(simp,[status(thm)],[6276]) ).
thf(6278,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ),
inference(pattern_uni,[status(thm)],[6277:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6309,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Oring ),
inference(simp,[status(thm)],[6278]) ).
thf(537,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
thf(2063,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(301,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
thf(1610,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(1742,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(795,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
thf(2549,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)],[795]) ).
thf(413,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
thf(1827,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
thf(1582,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(163,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
thf(1357,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(5263,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3009,1575]) ).
thf(5264,plain,
! [A: $i] :
( ( tc_nat @ ( c_1 @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) ),
inference(simp,[status(thm)],[5263]) ).
thf(5270,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_1 != c_0 )
| ( c_0 != A ) ),
inference(simp,[status(thm)],[5264]) ).
thf(5280,plain,
c_1 != c_0,
inference(simp,[status(thm)],[5270]) ).
thf(465,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_55) ).
thf(1925,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
thf(1597,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(134,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
thf(1299,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(689,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(2353,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)],[689]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
thf(1236,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(768,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
thf(2502,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(933,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
thf(2810,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(892,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
thf(2731,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(414,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
thf(1829,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(1012,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(2966,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(6294,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ~ $true
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(paramod_ordered,[status(thm)],[4231,1049]) ).
thf(6295,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__ring__1 )
!= ( C @ class_Ring__and__Field_Ocomm__ring__1 ) )
| ( C @ ( B @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(simp,[status(thm)],[6294]) ).
thf(6296,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ),
inference(pattern_uni,[status(thm)],[6295:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_IntDef_Oint @ ( D @ tc_fun ) ))]]) ).
thf(6316,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ class_Ring__and__Field_Ocomm__semiring__0__cancel ),
inference(simp,[status(thm)],[6296]) ).
thf(12837,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11029,1119]) ).
thf(12838,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( B @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( B @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[12837]) ).
thf(12839,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(pattern_uni,[status(thm)],[12838:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ ( D @ tc_fun ) @ tc_set ))]]) ).
thf(12855,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_fun ) @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ),
inference(simp,[status(thm)],[12839]) ).
thf(259,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_11) ).
thf(1532,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(953,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(2847,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(823,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
thf(2600,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(2898,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(lifteq,[status(thm)],[2897]) ).
thf(491,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).
thf(1976,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(5974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
!= ( v_x @ v_h ) )
| ( tc_nat != t_a )
| ( ( t_a @ ( C @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,5923]) ).
thf(5975,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != t_a )
| ( ( t_a @ ( C @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( B @ ( A @ ( v_x @ v_h @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[5974:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( v_x @ v_h ))]]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
thf(1550,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(3748,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != tc_nat )
| ~ ( D @ ( c_0 @ ( E @ c_less ) ) )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1575]) ).
thf(3749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( c_0 @ ( D @ c_less ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( tc_nat @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3748:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( tc_nat ))]]) ).
thf(3965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( c_0 @ ( D @ c_less ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ ( tc_nat @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(simp,[status(thm)],[3749]) ).
thf(464,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
thf(1923,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(789,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
thf(2539,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(353,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
thf(1713,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(758,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
thf(2484,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(443,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
thf(1885,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_22) ).
thf(1505,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(1399,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(644,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
thf(2270,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(306,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
thf(1621,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(5315,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2298,2414]) ).
thf(5316,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) ),
inference(simp,[status(thm)],[5315]) ).
thf(5333,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( c_0 @ c_Suc )
!= A )
| ( c_0 != A ) ),
inference(simp,[status(thm)],[5316]) ).
thf(5344,plain,
( ( c_0 @ c_Suc )
!= c_0 ),
inference(simp,[status(thm)],[5333]) ).
thf(578,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
thf(2138,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(861,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_11) ).
thf(2672,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(10051,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[9032,1667]) ).
thf(10052,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10051]) ).
thf(10072,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10052]) ).
thf(10086,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ c_plus ) ) )
!= c_0 )
| ( c_0 @ ( v_c @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10072]) ).
thf(3460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != t_a )
| ~ ( t_a @ ( t_a @ ( C @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(paramod_ordered,[status(thm)],[1618,1047]) ).
thf(3461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( t_a @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(pattern_uni,[status(thm)],[3460:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_a ))]]) ).
thf(803,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
thf(2563,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(475,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(1945,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)],[475]) ).
thf(945,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
thf(2832,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(733,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
thf(2436,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
thf(1416,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(11046,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10997,1119]) ).
thf(11047,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult )
!= ( A @ class_OrderedGroup_Ocomm__monoid__mult ) )
| ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(simp,[status(thm)],[11046]) ).
thf(11048,plain,
tc_nat @ tc_set @ class_OrderedGroup_Oab__semigroup__mult,
inference(pattern_uni,[status(thm)],[11047:[bind(A,$thf( tc_nat @ tc_set ))]]) ).
thf(383,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
thf(1769,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(742,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).
thf(2453,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(435,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).
thf(1870,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
thf(1331,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(299,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
thf(1606,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(337,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
thf(1681,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(973,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
thf(2887,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
thf(1184,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(870,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
thf(2690,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(221,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
thf(1463,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(535,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
thf(2059,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(7601,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Ring__and__Field_Opordered__comm__semiring )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1676,1275]) ).
thf(7602,plain,
( ( c_0 @ class_Ring__and__Field_Opordered__comm__semiring )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[7601:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
thf(1848,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
thf(1490,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(734,axiom,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(2438,plain,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(628,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_23) ).
thf(2238,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(946,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).
thf(2834,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(688,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).
thf(2351,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1026,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
thf(2993,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(607,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
thf(2191,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)],[607]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
thf(1204,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(1449,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(551,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_set @ ( C @ ( E @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( E @ ( D @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__intro_0) ).
thf(2087,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_set @ ( C @ ( E @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_in ) ) )
| ~ ( A @ ( E @ ( D @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_HOL_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(224,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
thf(1468,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(751,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
thf(2470,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(599,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
thf(2177,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(852,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).
thf(2655,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(32265,plain,
$false,
inference(e,[status(thm)],[2163,2612,2306,1767,1729,1899,1840,10081,2544,6845,2331,1295,2199,3021,2822,2630,1586,1501,1879,1337,2744,2889,1823,1190,2336,2109,2131,2031,1633,2778,1559,1105,2876,9833,2787,1850,1083,1982,2427,2480,1956,8077,12462,7549,1554,1110,9032,2250,2908,1618,2527,3012,1971,15780,5348,1041,2363,1200,2077,6142,1158,2512,4376,3072,12426,2210,2117,2940,1406,11256,7517,2622,1068,2808,2644,2495,2381,7641,1443,2659,9704,2953,2590,1401,1422,2947,1939,2248,3098,1073,1544,2676,2099,1591,1142,1269,1486,5501,1608,4090,1137,1872,12158,1327,2042,1507,2575,1497,3017,2195,1705,1078,1426,9127,2686,11029,1310,2740,2918,1735,11058,1164,2316,1275,2141,2476,1260,1988,2459,1761,3121,2580,7068,1063,1954,11055,9433,11549,1095,1196,1746,2723,1046,1935,1601,1803,2869,1887,2216,13452,9064,2046,5977,1914,2491,1127,2763,2985,2227,11382,1576,1650,1921,2886,1359,4030,1724,2173,6306,1366,2400,1967,2136,1518,1703,2531,2405,1623,1482,1254,2654,1055,1287,1709,4743,1323,2682,1279,5279,2328,2916,1792,1430,2735,7701,2698,1660,10997,4151,2755,14351,2444,1860,1264,1511,8834,2274,2185,1455,5182,3089,2488,1832,2897,5712,1992,2466,2126,1462,1059,1132,6208,3043,2571,8753,2713,1379,1147,1319,6310,2158,1773,2533,2169,2403,1087,1514,2373,4622,1347,1572,1115,2635,7728,1931,1568,7047,3014,2520,2730,6098,1641,2301,1815,1494,2989,1362,1963,1100,7509,1232,13715,2007,2950,1911,2650,1978,7677,1151,2777,1051,2017,2616,1465,1302,1664,2794,2324,2027,2105,3075,1811,7300,1373,1109,2893,7104,1418,2451,2236,2880,8929,1136,1858,1864,4050,2122,2291,1383,2254,1677,2034,1960,2555,1283,2073,2367,1377,1447,1351,12411,2002,1521,2205,1564,7413,2508,1169,5738,4033,2618,2281,11265,2861,1072,2523,1796,1119,2371,2979,1394,2772,2242,1345,2103,2750,1405,1943,1201,2804,2965,1104,1697,1242,2586,2884,2011,1206,2910,1691,1438,2646,1306,6684,1153,8795,13051,2641,1074,2922,11555,3459,1470,2093,1783,2737,6307,2296,2083,1067,2496,2790,12073,1868,2061,2000,1047,3037,1057,1163,1223,1091,6079,2596,1123,1666,2969,2937,2606,2414,2441,7730,2705,2264,2409,1387,1723,2733,1343,2560,1042,2541,2277,1355,1580,1570,1174,1676,2133,1217,2147,11223,1751,14772,8081,1619,1370,2396,11371,1238,2015,9158,1883,1560,2958,11570,5983,1920,2433,2565,1178,2179,1159,1079,1281,1392,1291,5285,2445,4295,2464,5879,2628,2670,2332,2826,2820,2872,1951,1687,1457,2068,1819,1836,1787,2181,1210,1656,3050,2345,1128,2547,2344,1740,1910,1106,7608,1360,1592,2515,2377,2895,2841,1064,1856,2694,7204,1755,2268,3001,1397,1234,1089,2498,1143,2115,1534,1794,2973,1121,2359,1375,1227,1111,2709,2692,1587,1096,1672,1540,3963,1878,2726,13163,1138,1719,11128,2858,2537,9063,11845,2638,1118,1329,1160,2561,1584,1937,2666,2781,2798,1683,1082,2023,2830,1182,2419,1075,1424,2312,3010,2455,1414,2053,2240,1842,1214,2349,2038,1446,2551,2085,1889,1644,1612,2472,7523,1155,1744,12859,1297,1131,1984,1874,1715,3005,2272,1825,2285,2504,2932,13415,1150,1478,1451,2304,1530,2836,2845,2598,1266,2153,2387,1231,1668,1974,1552,2851,2355,1192,1060,1050,2566,1799,7789,1947,4231,1852,2813,2766,2052,2482,1599,1246,2140,8980,3083,1759,1627,1525,1333,1434,2926,1086,1779,2208,1695,2963,1071,2915,2221,6311,2662,1202,2203,2702,2761,4195,2057,1846,1054,2748,1170,2408,2089,1895,1167,2189,1616,2995,2338,1996,2423,2529,2121,2413,3491,1273,2602,1595,11343,7785,1631,2260,1278,1906,2936,1135,1648,1727,6314,1146,2292,2391,2904,2556,1103,2033,2149,2717,1219,1747,11332,1548,1927,5882,5979,1154,1916,2981,1388,1965,1520,1124,2048,2938,7639,2225,2789,6312,1125,2525,2657,2849,2393,5923,1652,1929,9706,2674,2568,4605,2806,2991,5984,1403,1701,2398,5271,5350,1256,1488,1428,7201,1707,6532,2738,13093,2425,1258,7062,2573,11525,1139,1503,2193,5039,2029,2326,2891,1271,2308,3077,10083,1312,1635,1733,1058,1107,2759,2753,2055,1092,1765,1090,2457,1897,3091,2474,2510,1194,2521,1117,1574,2774,1542,2839,1122,2079,2361,6024,2721,2119,7783,1408,6308,2478,2151,2642,2229,2214,2383,2624,2415,9614,2493,2987,2906,1048,1349,9322,2097,1589,1933,2246,1492,1603,6321,2299,11268,1144,1771,15401,2945,5346,1043,1801,2856,2802,2197,1969,9129,2742,3055,12477,1162,2757,2785,1061,1667,2180,11078,2824,2025,2812,1080,2632,7699,1339,2610,2314,2129,7292,2111,1821,1731,12528,1862,7551,1838,1325,1149,6319,2874,1556,2542,1460,2289,2252,2664,1293,2553,2928,1381,2461,8079,7297,9327,1112,2578,11643,2365,1474,1044,2086,1176,11590,1113,2633,1496,1102,2207,1805,2770,2075,1198,9610,2439,2725,1699,2401,1594,2212,2171,2620,1445,1528,2064,2369,2244,2752,1775,2592,2535,9165,2101,1726,1364,2967,1250,2999,2156,2069,2867,2506,1562,12060,3009,1809,1304,1208,1467,2318,2652,2878,1134,1081,6076,1958,2899,2582,1049,2005,1076,2816,2914,3031,1662,2614,1166,2107,1905,1420,2124,2234,2449,1509,14406,1990,2684,6517,3455,1472,1145,2256,2942,2513,2298,2715,1961,11575,2661,1225,13047,11137,1098,2882,1516,2863,1070,11540,2977,2375,1156,1566,2143,1605,2588,1941,1252,2678,2518,1368,2175,1753,4894,3058,2407,1267,1484,2160,2569,13948,1790,2920,13089,1785,1262,1679,2044,1130,2468,1711,3019,3080,1499,1432,2165,1813,1637,2688,1188,2700,1186,3026,2429,4768,2276,1980,2128,6966,1317,1830,1763,11622,1901,1085,11081,6313,1658,2322,1538,2486,2545,1285,1738,2056,9505,3493,2379,1749,1372,2584,11017,1240,2411,2500,2838,2558,2113,1141,4133,1536,1221,2975,1353,2279,2357,2843,2145,1972,2320,1052,2711,1504,4431,1094,1140,7612,1670,1797,2728,1717,1881,1272,3007,2266,2865,2435,14732,1685,2696,1126,1108,2013,7089,2924,2626,1918,3457,1316,1084,5179,1459,2818,1180,1949,2870,2828,1817,2960,1321,1834,1913,2310,1844,2347,1654,1412,1781,1216,6674,2997,2490,2187,1390,2342,1575,1289,1453,5332,1866,2071,2775,1807,4310,2792,1998,3593,1276,2707,2167,1341,2853,1062,1101,13129,2971,1854,2526,2394,1646,2443,1385,2594,1721,2283,2389,1476,1674,2855,1639,1903,2135,1629,2004,2608,2431,3003,1244,9824,1523,1558,2934,2262,2447,2009,2956,2796,2912,9510,2462,1308,1513,2902,1442,1689,2081,2648,1777,1440,2330,2576,2066,1077,2162,2680,2183,1212,2095,11071,2036,1893,2294,1994,6499,2779,2019,5287,1161,1614,2421,2287,1642,1578,2155,1229,13133,1546,12117,2604,1876,1757,9070,3062,1116,1908,2930,2258,1133,2302,2517,5728,9034,2385,11035,7634,2983,2719,1097,11140,1395,1625,2815,1986,1527,1148,1673,1248,2050,2768,1480,2636,1436,2800,2334,6114,11231,6258,2091,1891,2223,2040,13377,2783,2201,4565,11595,1314,2746,12734,1335,1693,2070,11548,2704,1172,1410,2417,1056,1789,14828,1065,2340,2668,1165,9431,11784,11818,2021,6309,2063,1610,1742,2549,1827,1152,1582,1357,5280,1925,1597,1299,1120,1093,2353,1236,2502,2810,2731,1829,1129,2966,6316,12855,1532,2847,2600,2898,1976,5975,1550,3965,1923,2539,1713,2484,1885,1505,1399,11616,2270,1621,5344,2138,2672,10086,3461,2563,4891,1945,1737,2832,2436,1416,11048,1769,2453,1069,1870,1331,1606,1681,2887,1184,2690,1463,2059,7602,1848,1490,2438,2238,2834,2351,1088,2993,2191,1204,1449,11858,2087,1468,2470,2177,2655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42 % Computer : n009.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 22:09:46 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/1.39 % [INFO] Parsing done (392ms).
% 2.39/1.40 % [INFO] Running in sequential loop mode.
% 3.12/1.78 % [INFO] eprover registered as external prover.
% 3.12/1.79 % [INFO] Scanning for conjecture ...
% 3.59/1.99 % [INFO] Found a conjecture (or negated_conjecture) and 1414 axioms. Running axiom selection ...
% 4.72/2.26 % [INFO] Axiom selection finished. Selected 1036 axioms (removed 378 axioms).
% 5.67/2.46 % [INFO] Problem is propositional (TPTP CNF).
% 5.67/2.49 % [INFO] Type checking passed.
% 5.67/2.49 % [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 ...
% 132.62/34.83 % External prover 'e' found a proof!
% 132.62/34.83 % [INFO] Killing All external provers ...
% 132.62/34.83 % Time passed: 34272ms (effective reasoning time: 33423ms)
% 132.62/34.84 % Axioms used in derivation (1036): clsrel_Ring__and__Field_Osemiring__1__cancel_9, clsrel_Ring__and__Field_Oidom_20, clsrel_Ring__and__Field_Oordered__semiring__strict_5, clsrel_Ring__and__Field_Oordered__idom_3, clsrel_OrderedGroup_Ocancel__semigroup__add_1, clsarity_fun_31, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Oidom_17, clsarity_IntDef__Oint_57, clsrel_OrderedGroup_Olordered__ab__group__abs_3, clsrel_Ring__and__Field_Osemiring__1__cancel_12, clsrel_Ring__and__Field_Oordered__field_54, cls_Nat_Ole__0__eq__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, clsrel_Ring__and__Field_Opordered__comm__semiring_14, clsrel_Ring__and__Field_Opordered__ring_2, clsrel_Ring__and__Field_Oring__1_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19, cls_IntDiv_Ozdvd__0__right_0, clsrel_Ring__and__Field_Opordered__semiring_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, clsarity_IntDef__Oint_4, clsrel_Ring__and__Field_Oordered__field_7, clsrel_Ring__and__Field_Oordered__idom_32, cls_SetInterval_OlessThan__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6, clsrel_Ring__and__Field_Oordered__field_37, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13, clsrel_Ring__and__Field_Ocomm__ring_3, clsrel_Ring__and__Field_Opordered__semiring_6, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7, clsrel_Ring__and__Field_Oordered__semidom_16, clsrel_Ring__and__Field_Olordered__ring_14, clsrel_Ring__and__Field_Ocomm__semiring__0_2, cls_Set_OInterD_0, clsrel_OrderedGroup_Opordered__ab__group__add_6, clsarity_nat_32, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17, clsarity_nat_26, clsrel_Ring__and__Field_Olordered__ring_8, clsrel_Ring__and__Field_Ocomm__ring_12, clsrel_Ring__and__Field_Oordered__ring__strict_7, clsrel_Ring__and__Field_Osemiring__1__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring_4, clsarity_fun_29, clsrel_Ring__and__Field_Ocomm__semiring__1_12, clsrel_Ring__and__Field_Oordered__semiring__strict_22, clsrel_Ring__and__Field_Ocomm__semiring__1_15, clsrel_Ring__and__Field_Oordered__semidom_2, clsrel_Ring__and__Field_Oordered__field_48, clsarity_fun_13, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14, cls_SetsAndFunctions_Oset__plus__mono2_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_6, clsrel_Ring__and__Field_Osemiring__0__cancel_9, clsrel_Ring__and__Field_Ocomm__ring_17, clsarity_IntDef__Oint_45, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7, clsrel_OrderedGroup_Olordered__ab__group_13, cls_Divides_Omod__eq__0D__dest_0, clsrel_OrderedGroup_Olordered__ab__group__meet_1, cls_SetInterval_OatLeast__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__ring_6, clsrel_Ring__and__Field_Ocomm__semiring__1_3, clsrel_Ring__and__Field_Oordered__idom_43, clsrel_OrderedGroup_Olordered__ab__group_3, clsrel_Orderings_Olinorder_0, clsarity_fun_24, cls_Set_OsubsetI_1, clsrel_OrderedGroup_Olordered__ab__group_7, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oring_13, clsarity_nat_21, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22, clsrel_OrderedGroup_Opordered__ab__group__add_1, clsrel_OrderedGroup_Omonoid__mult_2, clsrel_Ring__and__Field_Oordered__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1, clsrel_OrderedGroup_Olordered__ab__group__join_3, cls_SetInterval_OgreaterThan__iff__iff2_0, clsrel_Ring__and__Field_Oordered__field_4, clsrel_OrderedGroup_Ocomm__monoid__add_2, clsrel_Ring__and__Field_Oordered__semidom_39, clsarity_IntDef__Oint_13, clsrel_Ring__and__Field_Oordered__idom_12, clsarity_nat_15, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4, clsrel_Ring__and__Field_Oordered__ring__strict_10, clsrel_Ring__and__Field_Olordered__ring_3, clsrel_Ring__and__Field_Oordered__idom_23, clsarity_IntDef__Oint_52, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_Ring__and__Field_Oidom_29, clsarity_IntDef__Oint_24, clsrel_Ring__and__Field_Oidom_26, clsrel_Ring__and__Field_Oring_10, clsrel_OrderedGroup_Osemigroup__add_0, clsrel_OrderedGroup_Olordered__ab__group_9, clsarity_set_9, clsarity_nat_10, clsrel_Ring__and__Field_Oordered__ring__strict_26, clsarity_nat_7, clsrel_Ring__and__Field_Oordered__semidom_9, cls_Orderings_Oorder__class_Oorder__trans_0, clsrel_Ring__and__Field_Oidom_13, clsrel_Ring__and__Field_Opordered__ring_14, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring__1_1, clsrel_Ring__and__Field_Oring__1_18, clsrel_OrderedGroup_Oab__group__add_6, clsrel_Ring__and__Field_Oordered__semidom_28, clsrel_Ring__and__Field_Oordered__semidom_34, clsrel_OrderedGroup_Olordered__ab__group__join_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, clsrel_Ring__and__Field_Opordered__ring_19, clsrel_OrderedGroup_Olordered__ab__group__abs_8, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10, clsarity_fun_6, clsrel_Ring__and__Field_Ocomm__ring__1_16, clsrel_Orderings_Olinorder_4, cls_Nat_Oless__Suc0__iff1_0, clsrel_Ring__and__Field_Osemiring__0__cancel_4, clsrel_Ring__and__Field_Oordered__idom_48, cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__semidom_23, clsrel_OrderedGroup_Olordered__ab__group__abs_18, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13, clsarity_nat_40, clsarity_IntDef__Oint_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4, clsrel_OrderedGroup_Olordered__ab__group__abs_13, clsrel_Ring__and__Field_Ocomm__ring__1_20, cls_IntDiv_Ozdvd__0__left__iff2_0, clsrel_Ring__and__Field_Osemiring__1__cancel_3, clsrel_Ring__and__Field_Oordered__semiring__strict_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add_1, clsrel_Ring__and__Field_Olordered__ring_4, clsrel_Ring__and__Field_Osemiring_1, clsrel_Ring__and__Field_Oordered__idom_37, clsrel_Ring__and__Field_Oordered__field_21, clsrel_Ring__and__Field_Oordered__ring__strict_22, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_Nat_Oadd__is__0__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6, clsrel_Ring__and__Field_Oordered__ring__strict_14, clsrel_Ring__and__Field_Oordered__idom_56, clsarity_IntDef__Oint_56, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21, clsrel_Ring__and__Field_Oidom_10, clsarity_set_2, clsarity_nat_25, clsrel_Ring__and__Field_Oordered__idom_17, clsrel_Ring__and__Field_Oring_6, clsrel_OrderedGroup_Olordered__ab__group__join_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8, clsrel_Ring__and__Field_Opordered__comm__semiring_3, clsrel_Ring__and__Field_Oring__1_19, clsrel_OrderedGroup_Oab__group__add_5, clsrel_Ring__and__Field_Olordered__ring_1, clsarity_nat_14, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsrel_Ring__and__Field_Oring__1_14, clsrel_Ring__and__Field_Ocomm__semiring__1_4, clsarity_nat_3, clsrel_Ring__and__Field_Ocomm__ring__1_5, clsarity_IntDef__Oint_3, cls_Nat_Onot__less0__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Oidom_1, cls_Nat_Oadd__gr__0__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10, clsrel_Ring__and__Field_Ocomm__ring__1_13, clsrel_OrderedGroup_Olordered__ab__group__meet_9, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8, clsrel_Ring__and__Field_Olordered__ring_21, clsrel_Ring__and__Field_Oaxclass__abs__if_0, clsrel_Ring__and__Field_Oordered__field_16, clsrel_Ring__and__Field_Ocomm__ring__1_7, cls_Nat_Oless__one__iff1_0, clsrel_Ring__and__Field_Ocomm__ring_9, clsrel_Ring__and__Field_Oordered__field_27, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25, cls_Set_OComplI_0, clsrel_OrderedGroup_Opordered__ab__group__add_8, clsarity_nat_29, cls_SetsAndFunctions_Oset__times__intro2_0, clsarity_IntDef__Oint_27, clsrel_Ring__and__Field_Opordered__cancel__semiring_3, clsrel_Ring__and__Field_Ocomm__ring__1_24, clsrel_Ring__and__Field_Ocomm__semiring__0_7, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__comm__semiring_8, clsrel_Ring__and__Field_Ocomm__ring__1_27, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10, clsrel_OrderedGroup_Oab__group__add_0, cls_Nat_Oneq0__conv__iff2_0, cls_Nat_Oadd__is__0__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__join_14, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1, clsrel_OrderedGroup_Opordered__ab__group__add_10, clsrel_Ring__and__Field_Oordered__idom_28, clsrel_Ring__and__Field_Oordered__field_38, clsrel_Ring__and__Field_Oordered__semiring__strict_19, clsarity_IntDef__Oint_0, clsrel_Ring__and__Field_Osemiring__1_4, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19, cls_SetsAndFunctions_Oset__times__mono2_0, clsarity_fun_19, cls_Set_OpsubsetI_0, cls_Set_Osubset__refl_0, clsrel_Ring__and__Field_Oordered__field_50, clsrel_Ring__and__Field_Oidom_21, clsarity_IntDef__Oint_49, clsarity_fun_3, clsrel_Ring__and__Field_Ocomm__ring_10, clsrel_Ring__and__Field_Ocomm__semiring__1_8, clsrel_Ring__and__Field_Opordered__comm__semiring_10, clsrel_Ring__and__Field_Opordered__ring_6, clsarity_IntDef__Oint_38, clsrel_Ring__and__Field_Oring_1, clsrel_Ring__and__Field_Oidom_7, clsrel_Ring__and__Field_Opordered__ring_11, clsrel_OrderedGroup_Oab__semigroup__mult_0, clsrel_Ring__and__Field_Opordered__semiring_2, clsrel_Ring__and__Field_Opordered__ring_22, clsrel_Ring__and__Field_Osemiring__0_2, clsrel_Ring__and__Field_Osemiring__1_10, clsrel_Ring__and__Field_Ocomm__ring_13, clsrel_Ring__and__Field_Oordered__idom_49, cls_Nat_OSuc__Suc__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_16, clsrel_Ring__and__Field_Oordered__field_43, clsrel_Ring__and__Field_Osemiring__0_7, clsarity_IntDef__Oint_35, clsrel_Ring__and__Field_Oordered__semidom_13, clsrel_OrderedGroup_Olordered__ab__group__meet_12, clsrel_Ring__and__Field_Oring__1_2, clsrel_Ring__and__Field_Olordered__ring_10, clsrel_Ring__and__Field_Oordered__field_8, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14, clsarity_IntDef__Oint_16, clsrel_Ring__and__Field_Oordered__semiring__strict_3, clsrel_Ring__and__Field_Oordered__field_59, cls_SetInterval_OlessThan__iff__iff1_0, clsrel_Ring__and__Field_Oordered__field_32, clsrel_Ring__and__Field_Oordered__semiring__strict_8, clsrel_OrderedGroup_Olordered__ab__group__abs_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4, clsrel_OrderedGroup_Olordered__ab__group__abs_10, clsarity_nat_36, clsrel_Ring__and__Field_Olordered__ring_25, clsrel_Ring__and__Field_Ocomm__ring_0, clsarity_nat_18, clsarity_fun_20, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, clsrel_Ring__and__Field_Osemiring__1__cancel_10, clsarity_nat_33, clsrel_Ring__and__Field_Oring__1_11, clsrel_Ring__and__Field_Osemiring__1_8, cls_SetInterval_OatMost__iff__iff2_0, clsrel_Ring__and__Field_Oordered__field_17, clsarity_IntDef__Oint_48, clsrel_OrderedGroup_Opordered__ab__group__add_11, clsarity_nat_22, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11, clsrel_Ring__and__Field_Oordered__semidom_24, clsarity_IntDef__Oint_19, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29, clsrel_Ring__and__Field_Oidom_6, clsrel_Ring__and__Field_Oordered__semiring__strict_16, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5, cls_Set_OPow__iff__iff2_0, cls_SetsAndFunctions_Oset__plus__mono3_0, clsrel_OrderedGroup_Olordered__ab__group_4, clsrel_Ring__and__Field_Osemiring__0_0, clsrel_Ring__and__Field_Oordered__semiring__strict_21, clsrel_Ring__and__Field_Oring__1_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add_4, clsrel_Ring__and__Field_Oordered__semidom_35, clsarity_IntDef__Oint_47, clsrel_Ring__and__Field_Oidom_25, clsrel_Ring__and__Field_Osemiring_2, clsrel_Ring__and__Field_Oordered__ring__strict_1, clsrel_Ring__and__Field_Opordered__cancel__semiring_9, clsrel_Ring__and__Field_Oordered__field_49, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8, cls_Nat_Ole__0__eq__iff2_0, clsrel_OrderedGroup_Ocomm__monoid__mult_3, cls_Set_OCompl__subset__Compl__iff__iff2_0, clsrel_Ring__and__Field_Opordered__ring_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2, clsrel_OrderedGroup_Olordered__ab__group__abs_14, clsrel_OrderedGroup_Olordered__ab__group_6, cls_SetsAndFunctions_Oset__times__intro_0, clsrel_OrderedGroup_Olordered__ab__group__abs_4, cls_Set_OsubsetI_0, clsrel_Ring__and__Field_Osemiring__1__cancel_4, clsrel_OrderedGroup_Olordered__ab__group__abs_5, clsrel_Ring__and__Field_Opordered__ring_3, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18, clsrel_Ring__and__Field_Oring__1_6, clsrel_Ring__and__Field_Oordered__idom_51, clsrel_Ring__and__Field_Osemiring__1_3, clsrel_Orderings_Olinorder_1, clsarity_IntDef__Oint_36, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9, clsarity_set_6, clsrel_Ring__and__Field_Ocomm__semiring_2, clsarity_IntDef__Oint_58, cls_Set_OCompl__eq__Compl__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12, clsrel_Ring__and__Field_Oordered__field_60, clsrel_Ring__and__Field_Oordered__idom_38, clsrel_Ring__and__Field_Oordered__idom_2, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__semidom_3, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5, clsarity_fun_7, clsarity_nat_11, clsrel_Ring__and__Field_Oordered__field_28, cls_Divides_Odvd__0__left__iff__iff2_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0, cls_OrderedGroup_Oabs__ge__self_0, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Ring__and__Field_Ocomm__ring__1_0, clsrel_Ring__and__Field_Oordered__field_53, clsrel_Ring__and__Field_Olordered__ring_15, clsrel_Ring__and__Field_Oring_9, clsrel_Ring__and__Field_Oordered__semiring__strict_11, clsarity_IntDef__Oint_53, cls_SetInterval_OatMost__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_36, clsarity_nat_27, clsrel_Ring__and__Field_Osemiring__0__cancel_3, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2, clsrel_Ring__and__Field_Ocomm__semiring_5, clsrel_Ring__and__Field_Oordered__idom_26, clsrel_Ring__and__Field_Osemiring__1__cancel_6, clsrel_Ring__and__Field_Oring__1_15, clsrel_Ring__and__Field_Oordered__ring__strict_8, clsrel_Ring__and__Field_Oordered__idom_52, clsrel_Ring__and__Field_Oordered__ring__strict_25, clsrel_Ring__and__Field_Opordered__semiring_7, clsrel_Ring__and__Field_Opordered__ring_13, clsrel_OrderedGroup_Opordered__ab__semigroup__add_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, clsrel_OrderedGroup_Ocomm__monoid__add_1, clsrel_Ring__and__Field_Oordered__ring__strict_27, clsrel_Ring__and__Field_Ocomm__semiring__1_14, clsarity_IntDef__Oint_14, clsrel_Ring__and__Field_Opordered__comm__semiring_13, clsarity_IntDef__Oint_7, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15, clsrel_OrderedGroup_Oab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring__1_10, clsrel_OrderedGroup_Olordered__ab__group_0, clsrel_Ring__and__Field_Oordered__field_10, clsarity_nat_16, clsrel_Ring__and__Field_Opordered__cancel__semiring_12, cls_SetInterval_OlessThan__subset__iff__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, clsrel_OrderedGroup_Olordered__ab__group_14, clsrel_Ring__and__Field_Oidom_14, clsarity_set_12, clsrel_Ring__and__Field_Ocomm__semiring__1_11, clsrel_Ring__and__Field_Oordered__idom_10, clsrel_OrderedGroup_Olordered__ab__group__meet_5, clsrel_Ring__and__Field_Osemiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__ring__strict_11, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, clsrel_Ring__and__Field_Ocomm__ring_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12, clsrel_Ring__and__Field_Olordered__ring_19, clsarity_IntDef__Oint_25, clsrel_Ring__and__Field_Oaxclass__0__neq__1_0, clsrel_Ring__and__Field_Ocomm__ring__1_21, clsrel_Ring__and__Field_Oordered__idom_47, clsrel_Ring__and__Field_Ocomm__ring_2, clsarity_nat_38, clsrel_Ring__and__Field_Oordered__ring__strict_5, clsrel_Ring__and__Field_Oordered__ring__strict_36, clsrel_Ring__and__Field_Oordered__field_39, cls_Set_OComplD__dest_0, clsrel_Ring__and__Field_Ocomm__semiring__0_3, clsrel_Ring__and__Field_Oordered__semidom_8, clsrel_Ring__and__Field_Oordered__idom_15, clsrel_Ring__and__Field_Ocomm__ring__1_19, clsrel_OrderedGroup_Olordered__ab__group_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3, clsrel_Ring__and__Field_Ocomm__ring__1_26, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11, clsrel_Ring__and__Field_Oordered__ring__strict_21, clsrel_Ring__and__Field_Oordered__idom_18, clsrel_Ring__and__Field_Ocomm__ring__1_4, cls_SetInterval_OatLeast__subset__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_16, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26, clsrel_Ring__and__Field_Ocomm__ring__1_14, clsrel_Ring__and__Field_Oordered__idom_31, cls_IntDiv_Ozdvd__triv__right_0, clsrel_Ring__and__Field_Opordered__semiring_1, cls_Nat_OZero__not__Suc__iff1_0, clsarity_fun_23, clsrel_Ring__and__Field_Olordered__ring_7, clsarity_IntDef__Oint_20, clsrel_Ring__and__Field_Oordered__field_46, cls_SetInterval_OatMost__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0, clsarity_fun_2, clsrel_Ring__and__Field_Oring_5, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19, clsrel_OrderedGroup_Olordered__ab__group__join_7, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5, clsrel_Ring__and__Field_Olordered__ring_26, clsrel_Ring__and__Field_Oordered__idom_22, clsrel_Ring__and__Field_Opordered__comm__semiring_2, clsrel_Ring__and__Field_Oordered__idom_57, clsrel_Ring__and__Field_Opordered__cancel__semiring_2, clsrel_OrderedGroup_Olordered__ab__group__meet_4, clsrel_Ring__and__Field_Opordered__ring_12, clsrel_Ring__and__Field_Osemiring__0_6, clsrel_Ring__and__Field_Oordered__ring__strict_4, cls_SetsAndFunctions_Oset__times__mono4_0, clsrel_Ring__and__Field_Ocomm__ring__1_25, clsarity_IntDef__Oint_2, clsarity_fun_12, clsrel_Ring__and__Field_Oordered__field_20, clsrel_OrderedGroup_Olordered__ab__group__join_13, clsrel_Ring__and__Field_Oordered__ring__strict_32, clsarity_IntDef__Oint_26, cls_Divides_Odvd__0__left__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_15, clsrel_Ring__and__Field_Ocomm__ring__1_15, clsarity_IntDef__Oint_31, clsrel_OrderedGroup_Oab__group__add_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15, clsrel_Ring__and__Field_Oordered__idom_11, clsrel_Ring__and__Field_Oordered__semidom_17, cls_Nat_OSuc__less__eq__iff2_0, clsrel_Ring__and__Field_Oordered__idom_29, clsrel_OrderedGroup_Olordered__ab__group__meet_6, clsrel_Ring__and__Field_Osemiring__1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_14, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_11, clsrel_Ring__and__Field_Oordered__field_35, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2, clsrel_Ring__and__Field_Oordered__field_42, cls_IntDiv_Ozdvd__triv__left_0, cls_Nat_Ozero__less__Suc_0, clsrel_Ring__and__Field_Opordered__ring_9, clsrel_Ring__and__Field_Opordered__cancel__semiring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_2, cls_Nat_Oless__Suc0__iff2_0, clsrel_Ring__and__Field_Ocomm__ring__1_8, clsrel_LOrder_Olorder_0, cls_Set_Osubset__antisym_0, clsrel_Ring__and__Field_Oring_2, cls_Set_OsubsetD_0, clsrel_Ring__and__Field_Oordered__idom_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9, clsrel_Ring__and__Field_Olordered__ring_22, clsarity_nat_37, clsrel_Ring__and__Field_Oordered__field_13, cls_Nat_Oadd__gr__0__iff2_1, clsrel_Ring__and__Field_Oaxclass__abs__if_1, clsrel_Ring__and__Field_Oidom_11, cls_SetsAndFunctions_Oset__plus__intro2_0, clsrel_Ring__and__Field_Ocomm__semiring__1_7, clsrel_Ring__and__Field_Oordered__semidom_31, clsrel_Ring__and__Field_Opordered__cancel__semiring_8, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Oordered__semiring__strict_17, clsarity_IntDef__Oint_15, clsrel_Ring__and__Field_Oidom_2, clsarity_set_14, clsrel_Ring__and__Field_Osemiring__1__cancel_5, clsrel_Ring__and__Field_Oordered__semidom_20, clsrel_OrderedGroup_Ocancel__semigroup__add_0, clsrel_Ring__and__Field_Oring__1_1, cls_SetInterval_OatLeast__iff__iff2_0, clsrel_Ring__and__Field_Osemiring__1__cancel_0, clsrel_OrderedGroup_Opordered__ab__group__add_2, clsrel_OrderedGroup_Olordered__ab__group__meet_11, clsrel_Ring__and__Field_Olordered__ring_11, clsarity_nat_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0, clsrel_Ring__and__Field_Ocomm__semiring__0_10, clsrel_Ring__and__Field_Opordered__ring_7, clsrel_Ring__and__Field_Oordered__field_24, clsrel_OrderedGroup_Oab__group__add_4, cls_IntDiv_Ozdvd__1__left_0, clsarity_IntDef__Oint_37, clsrel_Ring__and__Field_Oordered__idom_39, cls_SetInterval_OatMost__subset__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_6, clsrel_Ring__and__Field_Opordered__comm__semiring_9, clsrel_Ring__and__Field_Oordered__semidom_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5, clsrel_Ring__and__Field_Ocomm__ring_11, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6, clsarity_nat_0, clsarity_nat_43, clsrel_Orderings_Oorder_0, clsrel_Ring__and__Field_Oordered__field_31, clsarity_IntDef__Oint_42, clsrel_OrderedGroup_Ocomm__monoid__add_0, clsrel_Ring__and__Field_Osemiring__1_7, clsrel_Ring__and__Field_Oordered__field_29, clsrel_OrderedGroup_Olordered__ab__group__meet_13, clsrel_Ring__and__Field_Olordered__ring_18, clsrel_Ring__and__Field_Opordered__cancel__semiring_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_Ring__and__Field_Osemiring__0_1, clsrel_Ring__and__Field_Oaxclass__0__neq__1_1, clsrel_Orderings_Olinorder_2, clsarity_nat_34, cls_Set_ODiffE_0, clsrel_Ring__and__Field_Ocomm__semiring__1_10, clsrel_OrderedGroup_Olordered__ab__group_5, clsrel_Ring__and__Field_Opordered__ring_17, clsrel_OrderedGroup_Olordered__ab__group__abs_6, clsarity_fun_15, clsarity_fun_8, clsrel_OrderedGroup_Opordered__ab__semigroup__add_3, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3, cls_SetsAndFunctions_Oset__times__mono3_0, clsarity_IntDef__Oint_18, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12, clsrel_OrderedGroup_Olordered__ab__group__abs_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18, cls_SetInterval_OatMost__iff__iff1_0, clsrel_OrderedGroup_Olordered__ab__group__join_8, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8, clsrel_Ring__and__Field_Oordered__semidom_25, clsrel_OrderedGroup_Opordered__ab__group__add_4, clsrel_LOrder_Omeet__semilorder_0, clsarity_IntDef__Oint_29, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1, clsrel_OrderedGroup_Olordered__ab__group_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8, clsarity_fun_9, clsrel_Ring__and__Field_Olordered__ring_23, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6, clsrel_Ring__and__Field_Ocomm__semiring_1, clsrel_Ring__and__Field_Oordered__idom_46, clsrel_Ring__and__Field_Oordered__semidom_38, clsrel_OrderedGroup_Olordered__ab__group__meet_10, clsrel_Ring__and__Field_Oordered__idom_19, clsrel_OrderedGroup_Olordered__ab__group__meet_15, clsrel_Ring__and__Field_Olordered__ring_12, clsrel_Ring__and__Field_Osemiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_7, cls_Infinite__Set_Oatmost__one__unique_0, clsrel_OrderedGroup_Ocomm__monoid__mult_2, clsarity_nat_17, clsarity_set_1, clsrel_Ring__and__Field_Ocomm__ring__1_2, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4, clsrel_Ring__and__Field_Oidom_9, clsarity_set_7, cls_Divides_Odvd__triv__right_0, cls_Nat_OSuc__le__mono__iff1_0, clsrel_Ring__and__Field_Oordered__idom_14, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_35, clsrel_Ring__and__Field_Oordered__idom_20, clsrel_Ring__and__Field_Opordered__comm__semiring_12, clsrel_Ring__and__Field_Ocomm__ring_1, clsrel_OrderedGroup_Olordered__ab__group__join_11, clsrel_Ring__and__Field_Oordered__field_5, clsrel_Ring__and__Field_Opordered__comm__semiring_5, clsrel_Ring__and__Field_Opordered__cancel__semiring_5, clsrel_Ring__and__Field_Oordered__semidom_27, clsrel_Ring__and__Field_Oidom_15, clsrel_Ring__and__Field_Oordered__field_56, clsrel_Ring__and__Field_Oordered__semidom_36, clsrel_Ring__and__Field_Oidom_24, clsrel_Ring__and__Field_Oordered__semidom_4, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, clsrel_Ring__and__Field_Oordered__field_30, clsrel_Ring__and__Field_Ocomm__semiring_6, clsrel_Ring__and__Field_Oordered__field_58, cls_SetsAndFunctions_Oset__plus__intro_0, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_OrderedGroup_Olordered__ab__group__join_16, clsarity_IntDef__Oint_8, 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clsrel_Ring__and__Field_Oordered__ring__strict_23, clsrel_Ring__and__Field_Oordered__semiring__strict_23, clsrel_Ring__and__Field_Oordered__ring__strict_29, clsrel_Ring__and__Field_Oordered__ring__strict_6, clsrel_Ring__and__Field_Oring__1_17, clsrel_OrderedGroup_Opordered__ab__group__add_13, clsrel_Ring__and__Field_Oordered__semiring__strict_4, clsrel_Ring__and__Field_Opordered__comm__semiring_11, clsarity_IntDef__Oint_17, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3, cls_SetInterval_OatLeast__eq__iff__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsrel_OrderedGroup_Olordered__ab__group__abs_12, clsrel_OrderedGroup_Olordered__ab__group_12, clsrel_Orderings_Olinorder_3, clsarity_fun_28, clsrel_Ring__and__Field_Oordered__semidom_29, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_Ring__and__Field_Oordered__semidom_19, clsrel_Ring__and__Field_Osemiring__1__cancel_15, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, clsrel_Ring__and__Field_Osemiring__1_1, clsarity_IntDef__Oint_30, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3, clsrel_Ring__and__Field_Osemiring__0_4, clsrel_Ring__and__Field_Ocomm__ring_7, cls_Divides_Odvd__1__left_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10, clsarity_IntDef__Oint_39, clsrel_Ring__and__Field_Ocomm__ring_18, cls_IntDef_Onegative__zle_0, clsrel_OrderedGroup_Olordered__ab__group__abs_2, clsarity_nat_13, cls_SetInterval_OatLeast__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_13, clsarity_fun_14, clsrel_Ring__and__Field_Oordered__idom_0, clsrel_Ring__and__Field_Oordered__idom_45, clsrel_OrderedGroup_Opordered__ab__group__add_0, clsarity_IntDef__Oint_28, clsrel_Ring__and__Field_Oordered__field_6, clsrel_OrderedGroup_Omonoid__mult_1, clsrel_Ring__and__Field_Oordered__semidom_1, clsrel_Ring__and__Field_Oring__1_13, clsrel_Ring__and__Field_Osemiring__0__cancel_5, 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clsrel_OrderedGroup_Olordered__ab__group__join_9, clsrel_Ring__and__Field_Oordered__idom_6, clsarity_fun_17, clsrel_Ring__and__Field_Oidom_23, clsrel_Ring__and__Field_Olordered__ring_30, clsrel_Ring__and__Field_Oordered__idom_24, clsrel_Ring__and__Field_Opordered__cancel__semiring_10, clsrel_LOrder_Omeet__semilorder_1, clsrel_Ring__and__Field_Oidom_4, clsarity_set_0, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_Set_OPow__iff__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_4, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0, cls_Nat_OSuc__not__Zero__iff1_0, clsarity_nat_19, clsrel_Ring__and__Field_Ocomm__semiring_0, clsarity_nat_4, clsrel_Ring__and__Field_Oordered__semiring__strict_15, clsrel_Ring__and__Field_Ocomm__ring__1_6, clsrel_Ring__and__Field_Opordered__ring_5, clsrel_Ring__and__Field_Oordered__field_26, clsarity_fun_10, clsrel_Ring__and__Field_Oordered__idom_27, 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clsrel_OrderedGroup_Omonoid__mult_0, clsarity_IntDef__Oint_12, clsrel_Ring__and__Field_Opordered__cancel__semiring_13, clsrel_Ring__and__Field_Oidom_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28, clsrel_Ring__and__Field_Osemiring__0__cancel_8, cls_Set_OpsubsetE_1, clsarity_IntDef__Oint_55, clsrel_Ring__and__Field_Osemiring__0__cancel_1, clsrel_OrderedGroup_Opordered__ab__group__add_12, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, clsrel_Ring__and__Field_Oordered__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__semiring__1_1, clsrel_Ring__and__Field_Olordered__ring_20, clsarity_IntDef__Oint_50, clsrel_Ring__and__Field_Opordered__ring_21, clsrel_Ring__and__Field_Ocomm__semiring__1_5, clsrel_OrderedGroup_Oab__group__add_7, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2, clsarity_fun_21, clsrel_Ring__and__Field_Osemiring_4, clsrel_Ring__and__Field_Oordered__field_3, clsrel_Ring__and__Field_Oordered__field_15, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20, clsrel_Ring__and__Field_Oordered__idom_16, clsrel_Ring__and__Field_Osemiring__0_3, clsrel_OrderedGroup_Olordered__ab__group__join_5, clsrel_Ring__and__Field_Oring__1_16, clsrel_Ring__and__Field_Ocomm__ring__1_12, clsarity_nat_2, clsrel_OrderedGroup_Olordered__ab__group__meet_2, clsrel_Ring__and__Field_Ocomm__semiring__1_13, clsrel_Ring__and__Field_Olordered__ring_16, clsrel_Ring__and__Field_Opordered__comm__semiring_7, cls_Nat_OlessI_0, clsrel_Ring__and__Field_Oring__1_3, clsarity_nat_30, clsrel_Ring__and__Field_Oring__1_4, clsrel_OrderedGroup_Olordered__ab__group__abs_11, clsrel_Ring__and__Field_Osemiring__0__cancel_0, clsrel_Ring__and__Field_Oordered__semidom_14, clsrel_Ring__and__Field_Oordered__ring__strict_2, clsarity_nat_41, clsrel_Ring__and__Field_Oordered__ring__strict_30, clsrel_Ring__and__Field_Oordered__field_22, clsrel_Ring__and__Field_Oring__1_10, clsrel_Ring__and__Field_Oordered__field_33, clsrel_Ring__and__Field_Ocomm__ring__1_17, clsrel_Ring__and__Field_Ocomm__ring__1_28, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24, cls_SetsAndFunctions_Oset__plus__mono4_0, cls_IntDef_Onegative__zless_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0, clsrel_OrderedGroup_Olordered__ab__group__join_1, clsrel_Ring__and__Field_Oring_7, cls_IntDiv_Ozminus__dvd__iff__iff2_0, clsarity_IntDef__Oint_9, clsrel_Ring__and__Field_Opordered__comm__semiring_4, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7, clsrel_Ring__and__Field_Oordered__field_44, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0, cls_Nat_Onot__add__less2__iff1_0, clsarity_fun_18, clsrel_Ring__and__Field_Olordered__ring_24, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0, cls_SetInterval_OlessThan__subset__iff__iff1_0, clsrel_Ring__and__Field_Olordered__ring_27, clsrel_Ring__and__Field_Oordered__field_9, clsrel_Ring__and__Field_Oordered__field_11, cls_Set_ODiffE_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6, clsrel_Ring__and__Field_Olordered__ring_13, clsrel_OrderedGroup_Olordered__ab__group__join_18, clsarity_fun_4, clsrel_Ring__and__Field_Opordered__ring_16, clsarity_set_15, clsrel_Ring__and__Field_Oordered__semiring__strict_18
% 132.62/34.85 % No. of inferences in proof: 2893
% 132.62/34.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 34272 ms resp. 33423 ms w/o parsing
% 135.93/35.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 135.93/35.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------