TSTP Solution File: ANA029-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA029-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:08:53 EDT 2023
% Result : Unsatisfiable 107.90s 20.31s
% Output : Refutation 108.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 454
% Syntax : Number of formulae : 851 ( 179 unt; 58 typ; 0 def)
% Number of atoms : 1765 ( 356 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 6580 ( 940 ~; 972 |; 0 &;4668 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 58 usr; 9 con; 0-3 aty)
% Number of variables : 1270 ( 0 ^;1270 !; 0 ?;1270 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(v_k_type,type,
v_k: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(v_g_type,type,
v_g: $i > $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(v_f_type,type,
v_f: $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Orderings_Omax_type,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Parity_Oeven_type,type,
c_Parity_Oeven: $i > $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_Nat_Opower_type,type,
c_Nat_Opower: $i > $i > $i > $i ).
thf(class_Power_Orecpower_type,type,
class_Power_Orecpower: $i > $o ).
thf(c_Numeral_Onumber__of_type,type,
c_Numeral_Onumber__of: $i > $i > $i ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_1_type,type,
c_1: $i ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(c_IntDef_Oof__int_type,type,
c_IntDef_Oof__int: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group_type,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
thf(c_LOrder_Omeet_type,type,
c_LOrder_Omeet: $i > $i > $i > $i ).
thf(c_LOrder_Ojoin_type,type,
c_LOrder_Ojoin: $i > $i > $i > $i ).
thf(class_LOrder_Ojoin__semilorder_type,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_HOL_Oone_type,type,
class_HOL_Oone: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_List_Oreplicate_type,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_IntDef_Oneg_type,type,
c_IntDef_Oneg: $i > $i > $o ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_type,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_LOrder_Omeet__semilorder_type,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__join_type,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__meet_type,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_type,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_LOrder_Olorder_type,type,
class_LOrder_Olorder: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__abs__if_type,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_List_Ochar_OChar_type,type,
c_List_Ochar_OChar: $i > $i > $i ).
thf(c_OrderedGroup_Onprt_type,type,
c_OrderedGroup_Onprt: $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_type,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
thf(c_OrderedGroup_Opprt_type,type,
c_OrderedGroup_Opprt: $i > $i > $i ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_List_Olexn_type,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(tc_List_Ochar_type,type,
tc_List_Ochar: $i ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(194,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(809,plain,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(294,axiom,
class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
thf(1024,plain,
class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(361,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(1168,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
thf(846,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(1031,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(233,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(893,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(179,axiom,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
thf(777,plain,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_nat )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(324,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(1083,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(264,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(962,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(172,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(762,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(284,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
thf(1005,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(134,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(683,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(350,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(1142,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(131,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(677,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
thf(597,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(224,axiom,
class_Power_Orecpower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(873,plain,
class_Power_Orecpower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
thf(449,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ A @ C @ tc_nat ) )
| ( B = C )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ A @ C @ tc_nat ) )
| ( B = C )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(218,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(861,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(322,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(1078,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(67,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(533,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= ( c_times @ B @ c_0 @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(715,plain,
! [B: $i,A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= ( c_times @ B @ c_0 @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(197,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
thf(814,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_1 @ A )
| ( c_lessequals @ ( c_uminus @ c_1 @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
thf(698,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_1 @ A )
| ( c_lessequals @ ( c_uminus @ c_1 @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(164,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(747,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(257,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(945,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(315,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(1063,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
thf(930,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_HOL_Oabs @ B @ A )
= ( c_uminus @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_HOL_Oabs @ B @ A )
= ( c_uminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
thf(1127,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(181,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(782,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(841,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
thf(973,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_IntDef_Oint )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
thf(565,plain,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_IntDef_Oint )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_2) ).
thf(651,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(204,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(829,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
thf(404,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(310,axiom,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(1055,plain,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(83,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
thf(570,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Suc @ ( c_minus @ A @ ( c_Suc @ c_0 ) @ tc_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_1 @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
thf(719,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_1 @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(183,axiom,
class_Orderings_Olinorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(785,plain,
class_Orderings_Olinorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
thf(504,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(106,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).
thf(619,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
thf(1132,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(244,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(917,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ~ ( c_lessequals @ c_1 @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
thf(751,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ~ ( c_lessequals @ c_1 @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_1 @ ( c_uminus @ B @ A ) @ A )
| ( c_less @ B @ ( c_uminus @ c_1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
thf(638,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_1 @ ( c_uminus @ B @ A ) @ A )
| ( c_less @ B @ ( c_uminus @ c_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(353,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ c_0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
thf(1147,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ c_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
thf(1247,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( A = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
thf(969,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( A = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
thf(770,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
thf(416,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ B @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(332,axiom,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
thf(1100,plain,
! [A: $i] :
( ( c_minus @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(199,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(817,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
thf(902,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
thf(492,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
thf(789,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
thf(443,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( ( c_LOrder_Omeet @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
thf(623,plain,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( ( c_LOrder_Omeet @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
thf(514,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_1 @ B @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
thf(937,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_1 @ B @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
thf(475,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(247,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(924,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
thf(1136,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(207,axiom,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
thf(834,plain,
! [A: $i] :
( ( c_Nat_Opower @ A @ c_0 @ tc_IntDef_Oint )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(308,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(1051,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
!= ( c_uminus @ B @ A ) )
| ( c_0 = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
thf(905,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
!= ( c_uminus @ B @ A ) )
| ( c_0 = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(272,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(981,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(5,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(397,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(382,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
thf(1215,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(226,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
thf(877,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( B = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( B = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
= ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
= ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(178,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
= ( c_uminus @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
thf(774,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
= ( c_uminus @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
thf(411,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
thf(428,plain,
c_Parity_Oeven @ c_0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(334,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
thf(1104,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(1242,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
thf(849,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(378,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(1206,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(375,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
thf(1199,plain,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(171,axiom,
c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
thf(761,plain,
c_less @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(195,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
thf(810,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(317,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_1 != c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oone__neq__zero_0) ).
thf(1067,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_1 != c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(305,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(1047,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
thf(512,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
thf(439,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(202,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(825,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= ( c_times @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(952,plain,
! [B: $i,A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= ( c_times @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(219,axiom,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(862,plain,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
thf(424,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(139,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
thf(693,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
thf(429,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
thf(729,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(391,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
= ( c_HOL_Oabs @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
thf(1238,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
= ( c_HOL_Oabs @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(262,axiom,
! [A: $i] :
( ~ ( c_less @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
thf(957,plain,
! [A: $i] :
( ~ ( c_less @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_1 @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
thf(1223,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( ( c_LOrder_Ojoin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
thf(467,plain,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( ( c_LOrder_Ojoin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
thf(484,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(227,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
thf(879,plain,
class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
thf(889,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= ( c_IntDef_Oof__int @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= ( c_IntDef_Oof__int @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(1210,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(296,axiom,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(1027,plain,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( C = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( C = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(146,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(710,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( c_Nat_Opower @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_times @ A @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(288,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_0
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
thf(1012,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_0
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(335,axiom,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(1106,plain,
! [A: $i] :
( ( c_minus @ A @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
thf(852,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
thf(435,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(89,axiom,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).
thf(583,plain,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(290,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
thf(1017,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(104,axiom,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(615,plain,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(153,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
thf(725,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ c_0 @ B @ A )
= ( c_uminus @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
thf(869,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ c_0 @ B @ A )
= ( c_uminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
thf(989,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(857,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(61,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
thf(519,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( A = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
thf(742,plain,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_Suc @ c_0 ) )
| ( A = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
thf(578,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(225,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
thf(874,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(337,axiom,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
thf(1111,plain,
! [A: $i] :
( ( c_minus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ C @ A )
!= c_0 )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
thf(1227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ C @ A )
!= c_0 )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(14,axiom,
! [A: $i] :
( ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
thf(420,plain,
! [A: $i] :
( ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(471,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Opprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
thf(1028,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Opprt @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ c_1 @ A ) @ B @ A )
| ( c_less @ ( c_uminus @ B @ A ) @ c_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
thf(488,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ c_1 @ A ) @ B @ A )
| ( c_less @ ( c_uminus @ B @ A ) @ c_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
thf(933,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(368,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(1182,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( c_less @ c_0 @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
thf(669,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( c_less @ c_0 @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(116,axiom,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(642,plain,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(526,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
thf(590,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
| ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
thf(679,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_IntDef_Oint )
| ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ ( c_uminus @ c_1 @ A ) @ A )
| ( c_less @ c_1 @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
thf(547,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ ( c_uminus @ c_1 @ A ) @ A )
| ( c_less @ c_1 @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(144,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(706,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
thf(554,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(167,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(753,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(686,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_minus @ B @ C @ A ) @ A )
= ( c_minus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_minus @ B @ C @ A ) @ A )
= ( c_minus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(354,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(1150,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
thf(654,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(313,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(1060,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( c_less @ c_0 @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( c_less @ c_0 @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_0 @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
thf(779,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ B @ c_0 @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
thf(605,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(280,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(997,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(984,plain,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(241,axiom,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(911,plain,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(392,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(1241,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
thf(633,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(192,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(805,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
thf(657,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
thf(765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ C @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(362,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(1170,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
thf(674,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
thf(530,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_less @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
thf(662,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_less @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(248,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(926,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ c_0 @ ( v_k @ A ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(398,plain,
! [A: $i] : ( c_lessequals @ c_0 @ ( v_k @ A ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
thf(558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ ( c_minus @ B @ A @ tc_nat ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ ( c_minus @ B @ A @ tc_nat ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(187,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(794,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
thf(586,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(601,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
thf(819,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ c_1 @ A @ tc_nat )
| ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(238,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(904,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(285,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(1007,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ B @ c_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
thf(732,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ B @ c_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
thf(843,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_0 )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(772,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(147,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(711,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
thf(1124,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ A @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(10,axiom,
c_Parity_Oeven @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
thf(413,plain,
c_Parity_Oeven @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( ( c_minus @ A @ B @ tc_nat )
!= c_0 )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
thf(445,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ~ ( c_less @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(312,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(1058,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(328,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(1090,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
thf(919,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ C @ B @ tc_nat ) )
| ( A = C )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ C @ B @ tc_nat ) )
| ( A = C )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_less @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
thf(672,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_less @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(713,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
= ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
= ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ ( c_HOL_Oabs @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( ( c_Nat_Opower @ ( c_HOL_Oabs @ C @ A ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(205,axiom,
( ( c_Suc @ c_0 )
= ( c_times @ c_1 @ c_1 @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
thf(831,plain,
( ( c_Suc @ c_0 )
= ( c_times @ c_1 @ c_1 @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(133,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(681,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(182,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(784,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(287,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(1011,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(159,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(737,plain,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
thf(599,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(306,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(1048,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(158,axiom,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(736,plain,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ C @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
thf(451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ C @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_1) ).
thf(567,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( c_less @ c_0 @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Suc @ B ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
thf(509,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Nat_Opower @ c_0 @ ( c_Suc @ B ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= B )
| ( B = c_0 )
| ( C = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
thf(880,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= B )
| ( B = c_0 )
| ( C = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(119,axiom,
( c_1
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(649,plain,
( c_1
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(105,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(616,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(342,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(1122,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
thf(631,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(169,axiom,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(758,plain,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(198,axiom,
class_Power_Orecpower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(816,plain,
class_Power_Orecpower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_uminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
thf(700,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_uminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(964,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(365,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
thf(1177,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(314,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(1061,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( c_Orderings_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omax @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
thf(494,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omax @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ B @ c_1 @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
thf(1080,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ B @ c_1 @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(189,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
thf(799,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_1 @ ( c_uminus @ B @ A ) @ A )
| ( c_lessequals @ B @ ( c_uminus @ c_1 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
thf(943,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_1 @ ( c_uminus @ B @ A ) @ A )
| ( c_lessequals @ B @ ( c_uminus @ c_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(292,axiom,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(1022,plain,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
thf(912,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(2,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( v_g @ A ) @ ( v_k @ A ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(399,plain,
! [A: $i] : ( c_lessequals @ ( v_g @ A ) @ ( v_k @ A ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( B = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
thf(883,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ c_0 )
!= ( c_times @ A @ B @ tc_nat ) )
| ( B = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
thf(1015,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(282,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(1000,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(396,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(1250,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_minus @ B @ ( c_minus @ B @ A @ tc_nat ) @ tc_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(333,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
thf(1102,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(20,axiom,
~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
thf(431,plain,
~ ( c_Parity_Oeven @ c_1 @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(246,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
thf(922,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(381,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(1213,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
thf(768,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ B @ A ) @ C @ A ) @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(303,axiom,
class_LOrder_Ojoin__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(1044,plain,
class_LOrder_Ojoin__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
thf(563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
thf(473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(47,axiom,
class_HOL_Oone @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
thf(490,plain,
class_HOL_Oone @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
thf(426,plain,
! [B: $i,A: $i] :
( ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_minus @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(347,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(1134,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(196,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(812,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(165,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
thf(749,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(33,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(458,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
thf(1049,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ c_0 ) @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_1 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ c_0 @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_minus @ B @ c_0 @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(379,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(1208,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(87,axiom,
class_HOL_Oone @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
thf(580,plain,
class_HOL_Oone @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
thf(640,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ ( c_minus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(295,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(1025,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ B @ c_0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ B @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(386,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
thf(1225,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
thf(414,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ( c_Parity_Oeven @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(261,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
thf(954,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_minus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_minus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(318,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
thf(1070,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(223,axiom,
class_LOrder_Omeet__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(872,plain,
class_LOrder_Omeet__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
thf(409,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(388,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(1230,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
thf(1053,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(186,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
thf(791,plain,
c_0 != c_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
thf(1186,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
thf(441,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ ( c_uminus @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= C )
| ( C = c_0 )
| ( B = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_times @ B @ C @ A )
!= C )
| ( C = c_0 )
| ( B = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(717,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
thf(502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(390,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs @ c_1 @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
thf(1235,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs @ c_1 @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(37,axiom,
c_less @ c_0 @ c_1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
thf(470,plain,
c_less @ c_0 @ c_1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(345,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(1130,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
thf(1218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(384,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
thf(1220,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ B @ C @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ B @ C @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(293,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(1023,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(220,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(864,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(154,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(727,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= ( c_uminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= ( c_uminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
thf(595,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
thf(859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(277,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
thf(991,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ A ) @ B @ A ) @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
thf(978,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ A ) @ B @ A ) @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(325,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(1084,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(367,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(1180,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_minus @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
thf(539,plain,
! [B: $i,A: $i] :
( ( c_minus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_minus @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
thf(759,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_minus @ B @ c_1 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_less @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(371,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
thf(1189,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(336,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(270,axiom,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(976,plain,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
thf(688,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
thf(524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_minus @ B @ C @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
thf(581,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_minus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(91,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
thf(588,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_less @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_less @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4,negated_conjecture,
~ ( c_lessequals @ ( c_Orderings_Omax @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ c_0 @ t_b ) @ ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(401,plain,
~ ( c_lessequals @ ( c_Orderings_Omax @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ c_0 @ t_b ) @ ( c_HOL_Oabs @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
thf(995,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
thf(418,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_0) ).
thf(786,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
!= c_0 )
| ( ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ c_1 @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_times @ c_1 @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
thf(433,plain,
! [A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_nat )
| ~ ( c_Parity_Oeven @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(126,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(667,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(250,axiom,
class_LOrder_Olorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(929,plain,
class_LOrder_Olorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(41,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
thf(478,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ c_1 @ A ) @ B @ A )
| ( c_lessequals @ ( c_uminus @ B @ A ) @ c_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
thf(763,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ c_1 @ A ) @ B @ A )
| ( c_lessequals @ ( c_uminus @ B @ A ) @ c_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__eq__0__iff__number__of_0) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
thf(684,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
thf(536,plain,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(339,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(1116,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
thf(447,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(215,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
thf(854,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
thf(422,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ A @ tc_IntDef_Oint )
| ~ ( c_Parity_Oeven @ ( c_minus @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
thf(603,plain,
! [C: $i,B: $i,A: $i] :
( ( c_minus @ ( c_minus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_minus @ ( c_minus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(157,axiom,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(735,plain,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(281,axiom,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(999,plain,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(206,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(833,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(259,axiom,
( ( c_times @ c_1 @ c_1 @ tc_nat )
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
thf(950,plain,
( ( c_times @ c_1 @ c_1 @ tc_nat )
= ( c_Suc @ c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
!= ( c_IntDef_Oof__int @ B @ A ) )
| ( c_0 = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
!= ( c_IntDef_Oof__int @ B @ A ) )
| ( c_0 = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(190,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(801,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= c_1 )
| ( B
= ( c_uminus @ c_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
thf(506,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= c_1 )
| ( B
= ( c_uminus @ c_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(807,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
thf(437,plain,
! [B: $i,A: $i] :
( ~ ( c_Parity_Oeven @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ B @ tc_IntDef_Oint )
| ( c_Parity_Oeven @ A @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(263,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(960,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(316,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(1065,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(360,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
!= ( c_HOL_Oabs @ B @ A ) )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
thf(1165,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
!= ( c_HOL_Oabs @ B @ A ) )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(188,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Onprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
thf(796,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Onprt @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(363,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(1172,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(235,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(897,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(311,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(1056,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(125,axiom,
! [A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_uminus @ c_1 @ A ) @ A )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_1) ).
thf(664,plain,
! [A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_uminus @ c_1 @ A ) @ A )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(299,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
thf(1033,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(3,negated_conjecture,
~ ( c_lessequals @ c_0 @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(400,plain,
~ ( c_lessequals @ c_0 @ ( c_minus @ ( v_f @ v_x ) @ ( v_k @ v_x ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(230,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
thf(886,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(249,axiom,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(928,plain,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(161,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(740,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(275,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(987,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(85,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
thf(575,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Suc @ ( c_Numeral_Onumber__of @ A @ tc_nat ) )
= c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(355,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
thf(1152,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ C @ B @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
!= ( c_times @ C @ B @ A ) )
| ( B = c_0 )
| ( C = c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ c_1 @ A )
| ( c_less @ ( c_uminus @ c_1 @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
thf(528,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ c_1 @ A )
| ( c_less @ ( c_uminus @ c_1 @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ c_1 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
thf(908,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_times @ c_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(273,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(982,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(138,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(691,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(341,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(1120,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(53,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(501,plain,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(100,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(607,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(329,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(1093,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ ( c_uminus @ c_1 @ A ) @ A )
| ( c_lessequals @ c_1 @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
thf(839,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Oone @ A )
| ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ ( c_uminus @ c_1 @ A ) @ A )
| ( c_lessequals @ c_1 @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
thf(486,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(191,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(803,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(255,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_0 != c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) ).
thf(940,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( c_0 != c_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(253,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
thf(935,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(543,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( C = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ C @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ A ) @ A )
| ( C = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(130,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(676,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
thf(592,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_Parity_Oeven @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ C @ tc_nat ) @ A ) @ c_0 @ A )
| ( ( c_Numeral_Onumber__of @ C @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
thf(708,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(268,axiom,
class_LOrder_Olorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(972,plain,
class_LOrder_Olorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(48,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(491,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(327,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(1088,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(51733,plain,
$false,
inference(cvc4,[status(thm)],[645,809,629,1024,1168,846,1031,893,777,1083,962,762,1005,683,1073,1142,677,597,873,449,1041,861,1078,533,715,1233,814,698,747,945,1063,930,1196,1127,782,841,973,565,651,829,404,1055,570,719,785,504,619,1132,460,917,751,638,1147,1247,969,770,416,1100,817,902,492,789,443,623,514,937,475,924,1136,834,1051,821,905,480,981,397,1215,877,866,453,774,660,411,428,1201,1104,1242,849,1206,1199,761,810,1067,1047,512,439,825,952,862,1174,424,693,429,729,1238,957,1223,467,484,879,1178,889,1159,1210,1027,551,710,456,1012,1106,852,435,583,522,1017,615,725,869,989,857,519,742,578,874,1143,1111,1227,420,1118,471,1028,488,933,1182,669,642,526,590,679,547,706,554,753,686,1075,1150,738,654,1192,1060,1002,779,605,647,997,984,911,1086,1241,633,805,541,657,765,1170,674,530,662,926,398,1035,558,1071,794,586,745,573,601,1154,819,904,1007,732,843,772,711,1124,545,413,1139,445,611,1058,1090,919,947,672,713,498,1194,406,831,681,784,1011,737,599,1048,736,451,567,509,880,649,616,1122,631,758,816,609,700,895,964,626,1177,1061,494,1080,799,1162,943,1022,912,399,883,1015,1000,1250,1102,431,922,1213,768,827,695,636,1044,1113,563,473,722,490,426,1134,812,749,1145,754,458,836,1049,1203,1208,580,640,1025,1156,1225,414,954,993,1070,872,409,1230,1053,791,1186,441,1038,717,502,1235,463,470,1130,1218,1220,703,1023,613,864,727,1008,595,859,991,1094,978,1084,1180,556,539,482,759,891,1189,1108,976,688,524,581,588,517,401,1244,995,418,786,914,433,667,929,478,763,899,684,549,536,1045,1116,447,854,422,603,735,999,620,833,967,950,1097,801,506,807,437,960,1065,1165,796,1172,897,1056,664,1033,400,886,928,740,987,575,1152,1019,528,908,982,691,1120,501,607,1093,839,486,803,940,935,1184,543,560,676,592,496,708,972,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA029-1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 17:58:01 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.92/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.17/1.24 % [INFO] Parsing done (321ms).
% 2.17/1.25 % [INFO] Running in sequential loop mode.
% 2.61/1.44 % [INFO] eprover registered as external prover.
% 2.61/1.44 % [INFO] cvc4 registered as external prover.
% 2.67/1.45 % [INFO] Scanning for conjecture ...
% 3.16/1.60 % [INFO] Found a conjecture and 2804 axioms. Running axiom selection ...
% 4.19/1.83 % [INFO] Axiom selection finished. Selected 391 axioms (removed 2413 axioms).
% 4.34/1.93 % [INFO] Problem is propositional (TPTP CNF).
% 4.34/1.94 % [INFO] Type checking passed.
% 4.34/1.95 % [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 ...
% 107.90/20.29 % External prover 'cvc4' found a proof!
% 107.90/20.30 % [INFO] Killing All external provers ...
% 107.90/20.30 % Time passed: 19771ms (effective reasoning time: 19047ms)
% 107.90/20.30 % Solved by 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)>
% 107.90/20.30 % Axioms used in derivation (391): clsarity_IntDef__Oint_34, cls_NatSimprocs_Oequation__minus__iff__1_1, cls_Parity_Opower__less__zero__eq__number__of_0, cls_Nat_Onot__gr0_0, cls_OrderedGroup_Ojoin__0__eq__0_1, cls_Parity_Opower__le__zero__eq__number__of_1, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_Power_Opower__0__Suc_0, cls_OrderedGroup_Oneg__0__equal__iff__equal_0, cls_List_Odrop__replicate_0, cls_Power_Onat__zero__less__power__iff_2, cls_Nat_Onot__less0_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_OrderedGroup_Oneg__less__iff__less_1, cls_Nat_Oone__eq__mult__iff_0, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_OrderedGroup_Odiff__le__0__iff__le_0, cls_Parity_Opower__eq__0__iff__number__of_2, cls_Parity_Oeven__nat__power_2, clsrel_OrderedGroup_Olordered__ab__group__meet_1, cls_OrderedGroup_Oneg__le__iff__le_0, clsrel_Orderings_Olinorder_0, cls_Parity_Ozero__less__power__eq__number__of_4, cls_OrderedGroup_Odiff__self_0, cls_IntDef_Oof__int__0__le__iff_0, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oordered__idom_12, cls_Parity_Oeven__difference_2, cls_IntDef_Oof__int__0__less__iff_0, cls_Orderings_Olinorder__not__le_0, clsarity_IntDef__Oint_24, cls_Nat_Oless__one_1, cls_Parity_Oeven__nat__product_2, cls_NatSimprocs_Ominus__le__iff__1_1, clsarity_nat_7, cls_OrderedGroup_Oneg__0__le__iff__le_1, cls_OrderedGroup_Oneg__0__less__iff__less_0, cls_Nat_Odiff__is__0__eq_0, cls_Nat_Omult__le__cancel1_1, clsrel_OrderedGroup_Opordered__ab__group__add_1, cls_Parity_Oeven__nat__product_1, clsarity_IntDef__Oint_52, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_OrderedGroup_Opprt__eq__id_0, cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0, cls_OrderedGroup_Oneg__le__0__iff__le_1, cls_Nat_OSuc__Suc__eq_0, clsarity_nat_40, cls_Nat_Oop_A_K_Omult__0_0, cls_Power_Ozero__less__power__abs__iff_2, cls_Parity_Ozero__less__power__eq__number__of_1, cls_IntDiv_Ozero__less__zpower__abs__iff_2, cls_OrderedGroup_Oabs__ge__zero_0, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_0, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_OrderedGroup_Oabs__0__eq_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_OrderedGroup_Onprt__mono_0, cls_Nat_Oless__irrefl_0, cls_Nat_Odiff__le__self_0, cls_Nat_Odiff__0__eq__0_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_NatBin_Oeq__0__number__of_1, cls_NatSimprocs_Ole__minus__iff__1_1, cls_OrderedGroup_Oneg__meet__eq__join_0, cls_Ring__and__Field_Omult__cancel__left1_2, cls_NatBin_OSuc__nat__number__of_0, cls_IntDef_Oof__int__less__iff_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, cls_OrderedGroup_Odiff__le__0__iff__le_1, cls_Nat_Ozero__less__diff_1, clsrel_Ring__and__Field_Oaxclass__abs__if_0, clsrel_OrderedGroup_Oab__group__add_0, cls_List_Olength__drop_0, cls_Numeral_Obin__rel__simps__8_0, cls_Numeral_Obin__rel__simps__9_0, cls_Power_Opower_Osimps__2_0, cls_Parity_Opower__0__left__number__of_1, cls_Power_Opower__one__right_0, cls_Nat_Omult__less__cancel2_1, cls_Power_Opower__eq__0__iff_2, clsarity_IntDef__Oint_0, cls_List_Olength__replicate_0, cls_Parity_Oeven__power_2, cls_Nat_Omult__0__right_0, cls_LOrder_Ojoin__idempotent_0, cls_Ring__and__Field_Omult__cancel__right1_2, cls_List_Ochar_Oinject_0, cls_OrderedGroup_Omeet__0__eq__0_0, cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0, cls_Nat_Omult__less__cancel1_1, cls_Nat_Omult__eq__1__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_0, clsarity_IntDef__Oint_35, cls_Power_Ozero__le__power__abs_0, cls_OrderedGroup_Oabs__eq__0_0, clsarity_nat_36, cls_Nat_Oless__one_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_Nat_Odiff__Suc__Suc_0, clsarity_IntDef__Oint_47, clsarity_IntDef__Oint_48, cls_Nat_Omult__eq__1__iff_2, cls_Nat_Omult__le__cancel1_0, cls_Orderings_Omax__less__iff__conj_0, cls_IntDef_Oof__int__le__0__iff_1, cls_Parity_Oeven__neg_0, clsrel_OrderedGroup_Olordered__ab__group_6, clsrel_Orderings_Olinorder_1, cls_Parity_Ozero__less__power__nat__eq__number__of_1, clsarity_IntDef__Oint_58, cls_Parity_Ozero__le__power__eq__number__of_1, clsrel_Ring__and__Field_Oordered__idom_38, cls_Nat_Omult__less__cancel2_0, cls_IntDiv_Opower_Osimps__2_0, cls_Parity_Oeven__nat__power_0, cls_Parity_Ozero__less__power__nat__eq__number__of_0, clsrel_Ring__and__Field_Oordered__idom_51, cls_Power_Onat__one__le__power_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_Parity_Opower__le__zero__eq__number__of_5, clsrel_Ring__and__Field_Oordered__idom_36, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Ring__and__Field_Oordered__idom_52, clsrel_OrderedGroup_Olordered__ab__group_0, cls_Parity_Oeven__product_0, cls_Power_Ozero__less__power__abs__iff_0, cls_OrderedGroup_Ozero__le__pprt_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, cls_OrderedGroup_Oneg__0__less__iff__less_1, cls_Parity_Opower__eq__0__iff__number__of_1, cls_Parity_Oeven__nat__power_1, cls_OrderedGroup_Ojoin__0__eq__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0, cls_Power_Orecpower__class_Oaxioms__1_0, cls_IntDef_Oof__int__less__iff_1, cls_Orderings_Olinorder__not__le_1, cls_Nat_Omult__le__cancel2_2, cls_IntDef_Oof__int__0__le__iff_1, cls_Parity_Oeven__difference_1, cls_Parity_Opower__le__zero__eq__number__of_0, clsrel_OrderedGroup_Olordered__ab__group_17, cls_Power_Ozero__less__power__abs__iff_1, cls_Nat_Omult__cancel1_1, cls_OrderedGroup_Onprt__le__zero_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, cls_Nat_Onat__0__less__mult__iff_0, cls_IntDiv_Ozero__less__zpower__abs__iff_1, cls_IntDef_Oof__int__eq__iff_0, cls_IntDef_Oof__int__0__eq__iff_0, cls_Nat_Ole__0__eq_0, cls_Ring__and__Field_Omult__cancel__right1_1, cls_NatArith_Odiff__less_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_Nat_Ozero__less__diff_0, cls_OrderedGroup_Oneg__le__iff__le_1, cls_Power_Opower_Osimps__1_0, cls_Power_Opower__eq__0__iff_0, cls_Nat_OSuc__le__mono_0, cls_Ring__and__Field_Omult__cancel__left1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_6, cls_Parity_Opower__le__zero__eq__number__of_4, cls_Parity_Ozero__less__power__eq__number__of_3, cls_List_Odrop__0_0, cls_Nat_Oone__le__mult__iff_1, clsrel_Ring__and__Field_Oordered__idom_11, cls_Nat_OSuc__less__eq_1, clsrel_OrderedGroup_Olordered__ab__group__meet_17, cls_Parity_Oeven__nat__zero_0, cls_Nat_Omult__cancel2_0, cls_Nat_Omult__less__cancel1_0, cls_Parity_Opower__0__left__number__of_0, clsarity_nat_37, cls_OrderedGroup_Odiff__0_0, cls_Nat_Ozero__less__Suc_0, cls_Nat_Odiff__self__eq__0_0, clsrel_LOrder_Olorder_0, cls_NatSimprocs_Ole__minus__iff__1_0, clsarity_IntDef__Oint_37, cls_Ring__and__Field_Omult__cancel__left2_0, cls_Parity_Oeven__power_1, clsarity_nat_6, clsarity_nat_0, cls_NatBin_Oeq__nat__number__of_10, cls_Nat_Omult__cancel2_1, clsrel_OrderedGroup_Olordered__ab__group__abs_16, cls_Nat_Onat__0__less__mult__iff_1, clsrel_Power_Orecpower_3, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_Ring__and__Field_Oaxclass__0__neq__1_1, clsrel_Orderings_Olinorder_2, clsrel_OrderedGroup_Olordered__ab__group_1, clsarity_nat_45, clsrel_OrderedGroup_Olordered__ab__group__meet_15, cls_Nat_OSuc__diff__diff_0, cls_OrderedGroup_Opprt__0_0, clsarity_nat_34, cls_Parity_Ozero__less__power__nat__eq__number__of_2, cls_OrderedGroup_Ominus__minus_0, clsrel_Ring__and__Field_Oordered__idom_46, cls_OrderedGroup_Oabs__of__nonpos_0, cls_Nat_OSuc__le__mono_1, cls_OrderedGroup_Oneg__equal__0__iff__equal_0, clsarity_nat_17, cls_NatBin_Omult__nat__number__of_0, cls_IntDef_Oof__int__less__0__iff_0, cls_OrderedGroup_Opprt__eq__0_0, cls_Parity_Oeven__nat__Suc_1, cls_OrderedGroup_Opprt__mono_0, cls_OrderedGroup_Odiff__less__0__iff__less_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, clsarity_IntDef__Oint_54, cls_IntArith_Ozabs__less__one__iff_0, cls_Nat_Odiff__is__0__eq_H_0, clsarity_IntDef__Oint_40, clsrel_OrderedGroup_Olordered__ab__group__join_16, clsrel_Ring__and__Field_Oordered__idom_35, clsrel_Ring__and__Field_Oordered__idom_53, cls_OrderedGroup_Odiff__less__0__iff__less_1, cls_OrderedGroup_Oabs__minus__cancel_0, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_Parity_Opower__le__zero__eq__number__of_3, clsarity_IntDef__Oint_1, cls_Parity_Oodd__one_0, cls_NatSimprocs_Ominus__less__iff__1_0, cls_OrderedGroup_Ozero__less__abs__iff_1, cls_Nat_Oop_A_N_Odiff__0_0, cls_Orderings_Omax__less__iff__conj_1, cls_Parity_Opower__less__zero__eq__number__of_2, cls_OrderedGroup_Onprt__eq__0_0, cls_Parity_Oeven__difference_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_IntArith_Ozle__diff1__eq_0, cls_Nat_Oless__Suc0_0, cls_OrderedGroup_Ominus__diff__eq_0, clsrel_OrderedGroup_Olordered__ab__group__abs_1, cls_NatArith_Odiff__diff__cancel_0, cls_OrderedGroup_Oabs__eq__0_1, cls_Ring__and__Field_Omult__cancel__left1_0, cls_Parity_Oeven__product_1, cls_NatSimprocs_Oless__minus__iff__1_1, clsrel_OrderedGroup_Olordered__ab__group_15, clsrel_Ring__and__Field_Oordered__idom_41, clsarity_IntDef__Oint_32, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_Nat_Omult__cancel1_0, cls_Parity_Ozero__less__power__eq__number__of_2, cls_OrderedGroup_Oabs__le__zero__iff_0, cls_Parity_Oeven__power_0, clsarity_IntDef__Oint_22, cls_Nat_OOne__nat__def_0, cls_Nat_Omult__le__cancel2_1, cls_OrderedGroup_Oneg__less__0__iff__less_1, cls_Nat_Odiff__Suc__less_0, clsarity_nat_5, cls_Ring__and__Field_Oone__neq__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_2, cls_Nat_Oone__eq__mult__iff_2, cls_Nat_Omax__Suc__Suc_0, cls_Power_Onat__zero__less__power__iff_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9, clsrel_Ring__and__Field_Oordered__idom_8, cls_IntDiv_Ozero__less__zpower__abs__iff_0, cls_Nat_Onot__gr0_1, clsarity_IntDef__Oint_43, cls_NatSimprocs_Ominus__le__iff__1_0, cls_OrderedGroup_Odiff__0__right_0, clsrel_Ring__and__Field_Opordered__comm__semiring_15, cls_Ring__and__Field_Oabs__one_0, cls_IntDef_Oof__int__eq__0__iff_0, clsarity_nat_9, cls_Ring__and__Field_Omult__cancel__right2_0, cls_Nat_Oone__le__mult__iff_0, cls_OrderedGroup_Oneg__less__iff__less_0, cls_Parity_Ozero__less__power__eq__number__of_5, clsarity_IntDef__Oint_33, cls_Parity_Ozero__le__power__eq__number__of_0, cls_Nat_Omax__0L_0, cls_Parity_Oeven__zero_0, cls_IntArith_Ozabs__less__one__iff_1, cls_Parity_Opower__less__zero__eq__number__of_1, clsrel_Ring__and__Field_Oordered__idom_4, clsrel_Power_Orecpower_2, cls_Parity_Opower__le__zero__eq__number__of_2, cls_NatSimprocs_Ominus__less__iff__1_1, cls_OrderedGroup_Oneg__0__equal__iff__equal_1, cls_IntDef_Oof__int__le__iff_1, cls_IntDef_Oof__int__le__0__iff_0, cls_OrderedGroup_Oabs__0__eq_1, clsarity_IntDef__Oint_17, cls_IntDef_Oof__int__0__less__iff_1, clsrel_Ring__and__Field_Oordered__idom_33, cls_Nat_Oless__Suc0_1, cls_OrderedGroup_Onprt__0_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, cls_Power_Opower__eq__0__iff_1, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Power_Orecpower_9, clsrel_OrderedGroup_Olordered__ab__group_2, cls_IntDef_Oof__int__less__0__iff_1, cls_Nat_OSuc__not__Zero_0, clsrel_OrderedGroup_Opordered__ab__group__add_13, cls_OrderedGroup_Odiff__eq__0__iff__eq_0, cls_Nat_Omult__less__cancel1_2, cls_OrderedGroup_Oneg__equal__0__iff__equal_1, cls_IntDiv_Ozero__le__zpower__abs_0, cls_IntDef_Oof__int__0__eq__iff_1, clsrel_Ring__and__Field_Oordered__idom_13, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_OrderedGroup_Opordered__ab__group__add_0, cls_Parity_Oeven__nat__Suc_0, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, clsrel_OrderedGroup_Olordered__ab__group__abs_2, clsarity_nat_13, clsrel_Ring__and__Field_Oordered__idom_34, cls_Ring__and__Field_Omult__cancel__right1_0, cls_Nat_Oone__le__mult__iff_2, cls_Parity_Ozero__less__power__eq__number__of_0, cls_OrderedGroup_Oneg__equal__iff__equal_0, clsrel_OrderedGroup_Olordered__ab__group__join_15, cls_Power_Opower__one_0, cls_Parity_Oeven__nat__product_0, clsarity_nat_24, cls_List_Olexn_Osimps__1_0, cls_OrderedGroup_Oneg__le__0__iff__le_0, clsarity_IntDef__Oint_51, cls_IntArith_Ozle__diff1__eq_1, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_Nat_Ole0_0, cls_Nat_OSuc__less__eq_0, cls_Parity_Opower__eq__0__iff__number__of_0, clsarity_nat_4, cls_OrderedGroup_Oneg__0__le__iff__le_0, clsarity_IntDef__Oint_23, cls_Parity_Oeven__difference_3, clsrel_OrderedGroup_Ocomm__monoid__mult_4, clsarity_IntDef__Oint_63, cls_IntDiv_Opower_Osimps__1_0, cls_IntDef_Oint__0__neq__1_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, cls_OrderedGroup_Oneg__less__0__iff__less_0, cls_Nat_Ole__0__eq_1, clsrel_OrderedGroup_Omonoid__mult_0, cls_List_Ochar_Oinject_1, cls_OrderedGroup_Oabs__of__nonneg_0, cls_Nat_Omult__le__cancel1_2, cls_Parity_Oeven__product_2, clsrel_Power_Orecpower_16, cls_Nat_Omult__le__cancel2_0, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, clsarity_IntDef__Oint_50, cls_Orderings_Omax__less__iff__conj_2, clsrel_OrderedGroup_Olordered__ab__group__meet_2, cls_Nat_OZero__not__Suc_0, cls_Nat_OlessI_0, cls_IntDef_Oof__int__eq__0__iff_1, cls_OrderedGroup_Oabs__idempotent_0, cls_OrderedGroup_Oabs__le__zero__iff_1, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1, cls_NatSimprocs_Oless__minus__iff__1_0, cls_NatSimprocs_Oequation__minus__iff__1_0, cls_Nat_Omult__less__cancel2_2, cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0, cls_Nat_OSuc__pred_0, cls_Nat_Omult__eq__1__iff_1, cls_NatBin_Oeq__number__of__0_1, cls_Nat_Omult__is__0_0, cls_List_Ochar_Osize_0, cls_Parity_Ozero__le__power__eq__number__of_2, cls_Parity_Opower__even__abs__number__of_0, cls_Parity_Oeven__neg_1, cls_OrderedGroup_Omeet__0__eq__0_1, cls_OrderedGroup_Oneg__join__eq__meet_0, clsrel_OrderedGroup_Olordered__ab__group__join_1, clsarity_IntDef__Oint_9, cls_Nat_Omax__0R_0, cls_Nat_Oone__eq__mult__iff_1, cls_Power_Onat__zero__less__power__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_18
% 107.90/20.31 % No. of inferences in proof: 793
% 107.90/20.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19771 ms resp. 19047 ms w/o parsing
% 107.95/20.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 108.20/20.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------