%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA009-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:50:15 AM UTC 2026
% Result : Unsatisfiable 13.17s 3.52s
% Output : Refutation 14.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 299
% Syntax : Number of formulae : 599 ( 139 unt; 0 typ; 0 def)
% Number of atoms : 1199 ( 214 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 4336 ( 596 ~; 600 |; 0 &;3140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 8 con; 0-3 aty)
% Number of variables : 922 ( 0 ^; 922 !; 0 ?; 922 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_lb_decl,type,
v_lb: $i > $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(c_IntDef_Oof__int_decl,type,
c_IntDef_Oof__int: $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Numeral_Onumber__of_decl,type,
c_Numeral_Onumber__of: $i > $i > $i ).
thf(c_Nat_Opower_decl,type,
c_Nat_Opower: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_IntDef_Oneg_decl,type,
c_IntDef_Oneg: $i > $i > $o ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group_decl,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
thf(c_LOrder_Omeet_decl,type,
c_LOrder_Omeet: $i > $i > $i > $i ).
thf(c_LOrder_Ojoin_decl,type,
c_LOrder_Ojoin: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__join_decl,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__meet_decl,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_LOrder_Omeet__semilorder_decl,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_LOrder_Olorder_decl,type,
class_LOrder_Olorder: $i > $o ).
thf(c_List_Odrop_decl,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__abs__if_decl,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_List_Ochar_OChar_decl,type,
c_List_Ochar_OChar: $i > $i > $i ).
thf(c_OrderedGroup_Onprt_decl,type,
c_OrderedGroup_Onprt: $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_decl,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
thf(c_OrderedGroup_Opprt_decl,type,
c_OrderedGroup_Opprt: $i > $i > $i ).
thf(c_List_Oupt_decl,type,
c_List_Oupt: $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_decl,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Ochar_decl,type,
tc_List_Ochar: $i ).
thf(c_List_Olexn_decl,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(230,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(760,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(162,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(628,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(287,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(893,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(518,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_List_Oupt ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_List_Oupt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_List_Oupt ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_List_Oupt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
thf(481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(523,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(215,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(730,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(379,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(104,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
thf(511,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
thf(677,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(533,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_13) ).
thf(500,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(246,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_uminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
thf(797,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_uminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(254,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(814,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(20,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(340,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( tc_List_Ochar @ ( B @ ( A @ c_List_Ochar_OChar ) @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( tc_List_Ochar @ ( B @ ( A @ c_List_Ochar_OChar ) @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(2,negated_conjecture,
! [A: $i] : ( t_b @ ( t_b @ ( A @ v_g @ ( A @ v_lb @ c_plus ) ) @ ( A @ v_f @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(301,plain,
! [A: $i] : ( t_b @ ( t_b @ ( A @ v_g @ ( A @ v_lb @ c_plus ) ) @ ( A @ v_f @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
thf(565,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
thf(841,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_0 @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(57,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_15) ).
thf(417,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(132,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
thf(570,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(504,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( A @ ( C @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(542,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(587,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(619,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= ( A @ ( C @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
thf(838,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= ( A @ ( C @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(297,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(917,plain,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(199,axiom,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(702,plain,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(226,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(751,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
thf(902,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Omeet ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Ojoin ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Omeet ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Ojoin ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(606,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(881,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= ( A @ ( B @ c_uminus ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(448,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
thf(789,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) @ c_HOL_Oabs ) )
= ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(170,axiom,
tc_nat @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(646,plain,
tc_nat @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
thf(514,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(89,axiom,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(480,plain,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(177,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(660,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= B )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= B )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(602,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
thf(766,plain,
! [B: $i,A: $i] :
( ( c_0 = B )
| ( c_0
!= ( A @ ( B @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(46,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(397,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(192,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
thf(687,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(6,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(307,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(452,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(67,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
thf(439,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
thf(761,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(39,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(381,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_times ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
thf(546,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_times ) ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(793,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(294,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(910,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Onprt ) )
= c_0 )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(3,negated_conjecture,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_lb @ c_uminus ) @ ( v_x @ v_f @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(302,plain,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_lb @ c_uminus ) @ ( v_x @ v_f @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(147,axiom,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(598,plain,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(127,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(561,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_times ) ) @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(60,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(424,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
thf(630,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Ojoin ) ) )
= B )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Ojoin ) ) )
= B )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(82,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(467,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(461,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(94,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(493,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(229,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(757,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
thf(682,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(122,axiom,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
thf(551,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
= c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
thf(456,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(269,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(852,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(435,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(138,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(583,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(697,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Oabs ) )
= B )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
thf(317,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( c_0 @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(172,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(650,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(725,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(221,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(742,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( c_0
!= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
thf(578,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( c_0
!= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(283,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(884,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
thf(537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Ochar_OChar ) )
!= ( D @ ( C @ c_List_Ochar_OChar ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_uminus ) )
!= ( A @ ( C @ c_uminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_uminus ) )
!= ( A @ ( C @ c_uminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(526,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(143,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_14) ).
thf(590,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ( A @ tc_set @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Omeet ) ) )
= B )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
thf(679,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_LOrder_Omeet ) ) )
= B )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(554,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
thf(753,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(191,axiom,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(686,plain,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
thf(476,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
thf(647,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(654,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= ( tc_nat @ ( B @ ( c_0 @ c_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(633,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_times ) ) )
= ( tc_nat @ ( B @ ( c_0 @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
thf(805,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(102,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(508,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(175,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(657,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Opprt ) @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
thf(558,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Opprt ) @ ( A @ ( B @ c_OrderedGroup_Opprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(113,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
thf(530,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_uminus ) @ c_plus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_uminus ) @ c_plus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(140,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(586,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(178,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(662,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(208,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(718,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(888,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
thf(425,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(856,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Onprt ) @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_OrderedGroup_Onprt ) @ ( A @ ( B @ c_OrderedGroup_Onprt ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
thf(733,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(149,axiom,
tc_IntDef_Oint @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(601,plain,
tc_IntDef_Oint @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
thf(584,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(256,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(819,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Ojoin ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Ojoin ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(196,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
thf(694,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(222,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(743,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(54,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
thf(413,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(204,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(711,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(298,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_IntDef_Oof__int ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
thf(919,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_IntDef_Oof__int ) )
= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(350,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_times ) ) @ ( tc_nat @ ( A @ ( C @ c_times ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( C @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(184,axiom,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(672,plain,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
thf(611,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
thf(787,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ ( B @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(206,axiom,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
thf(713,plain,
! [A: $i] :
( ( A @ ( c_0 @ ( A @ ( c_0 @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_OrderedGroup_Opprt ) )
= c_0 )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(419,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(130,axiom,
tc_nat @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(567,plain,
tc_nat @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(509,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
thf(599,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
thf(764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( B @ ( D @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(151,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
thf(604,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(156,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
thf(616,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(4,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(303,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Omeet ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_LOrder_Omeet ) ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(252,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(811,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
thf(494,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(116,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
thf(535,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( B @ ( c_0 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( B @ ( c_0 @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(145,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(594,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( B @ ( C @ c_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_0 )
| ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( B @ ( C @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(288,axiom,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
thf(895,plain,
! [A: $i] :
( ( c_0
= ( A @ ( c_0 @ c_IntDef_Oof__int ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(161,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(626,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(234,axiom,
! [A: $i] :
( ~ ( A @ ( c_0 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
thf(769,plain,
! [A: $i] :
( ~ ( A @ ( c_0 @ c_IntDef_Oneg ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(182,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(668,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(700,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(912,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_Nat_Opower ) ) )
= ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( c_0 @ c_Nat_Opower ) ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(563,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( c_0 @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(210,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(722,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Ojoin ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Omeet ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_LOrder_Ojoin ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_LOrder_Omeet ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(142,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(589,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(531,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(795,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(179,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(663,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_plus ) ) )
= ( tc_nat @ ( B @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_plus ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(157,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(617,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(516,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(76,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
thf(458,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(258,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_uminus ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
thf(823,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_uminus ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(237,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(776,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(110,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(525,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(205,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(712,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(194,axiom,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(690,plain,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( C @ ( A @ c_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(705,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_times ) ) )
!= ( tc_nat @ ( C @ ( A @ c_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(55,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(414,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(185,axiom,
! [A: $i] :
( ( c_0
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
thf(673,plain,
! [A: $i] :
( ( c_0
= ( tc_nat @ ( A @ c_Numeral_Onumber__of ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Numeral_Onumber__of ) @ c_IntDef_Oneg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( A @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
thf(502,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(79,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(463,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(470,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(168,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(643,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(544,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
thf(907,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_0 @ ( B @ c_plus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_plus ) ) @ c_uminus ) )
= ( A @ ( A @ ( C @ c_uminus ) @ ( A @ ( B @ c_uminus ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(703,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(613,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(213,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(727,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ c_Numeral_Onumber__of ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_Numeral_Onumber__of ) @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_plus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_plus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(446,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
thf(571,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_IntDef_Oof__int ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
thf(465,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= ( tc_nat @ ( c_0 @ ( B @ c_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_times ) ) )
= ( tc_nat @ ( c_0 @ ( B @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(193,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(688,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_lessequals ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
thf(844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( B @ c_plus ) ) @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(771,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(31,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(363,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_times ) ) @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(173,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(652,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
thf(390,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_0 @ ( A @ ( B @ c_HOL_Oabs ) @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(216,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(731,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
thf(568,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
thf(478,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( A @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( B @ c_uminus ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
thf(346,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
thf(549,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( B @ c_less ) ) )
| ~ ( A @ ( c_0 @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_IntDef_Oof__int ) )
!= c_0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( c_0 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
thf(832,plain,
! [B: $i,A: $i] :
( ( c_0
= ( A @ ( c_0 @ ( B @ c_times ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
thf(684,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_lb @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(300,plain,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_lb @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
thf(432,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_uminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(263,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Ojoin ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
thf(835,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Ojoin ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(50,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).
thf(405,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(854,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(276,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(867,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(865,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_less ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(218,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(735,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_IntDef_Oof__int ) @ ( A @ ( B @ c_IntDef_Oof__int ) @ c_less ) ) )
| ~ ( tc_IntDef_Oint @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
thf(506,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
thf(437,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(474,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(664,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(635,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ c_HOL_Oabs ) )
= ( A @ ( B @ c_HOL_Oabs ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
thf(720,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(29,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
thf(358,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( tc_IntDef_Oint @ ( c_0 @ c_HOL_Oabs ) @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(807,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
thf(886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(415,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(160,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_12) ).
thf(624,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_set @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(80,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(464,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(17,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
thf(332,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(575,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_HOL_Oabs ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
thf(427,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_uminus ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
thf(860,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( A @ ( B @ c_uminus ) )
!= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(596,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
thf(528,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
thf(644,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(723,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(68,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(442,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(278,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Omeet ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
thf(871,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_0 @ c_uminus ) @ ( c_0 @ c_LOrder_Omeet ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(34,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(369,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(214,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(728,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(220,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(740,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(91,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(486,plain,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(248,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(803,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(19,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(337,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(126,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
thf(560,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
thf(592,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(202,axiom,
tc_nat @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(708,plain,
tc_nat @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( B @ c_Nat_Opower ) ) @ ( c_0 @ c_less ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(176,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
thf(659,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(755,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(186,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(676,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
thf(496,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
thf(454,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1254,plain,
$false,
inference(e,[status(thm)],[809,365,760,846,628,893,518,468,666,481,352,408,523,730,379,511,677,385,533,500,797,715,472,814,747,340,898,709,301,565,841,417,570,504,344,542,587,619,838,917,702,751,902,638,421,606,881,325,448,789,443,321,376,646,514,348,821,480,660,411,849,312,602,766,397,687,307,452,439,761,381,546,793,910,778,302,598,561,392,424,630,429,467,361,879,329,461,493,757,682,551,456,852,435,583,830,697,874,317,650,725,403,388,356,869,742,578,884,537,669,526,590,679,554,753,686,476,647,738,654,371,633,805,508,657,558,530,773,586,662,718,888,425,856,573,733,601,584,819,904,694,743,413,826,711,335,919,350,672,611,787,713,498,784,419,567,509,599,863,764,604,900,406,616,303,890,811,494,535,816,323,594,621,895,626,769,668,858,367,700,520,912,399,608,394,563,922,722,490,589,531,795,663,487,812,749,342,617,516,458,823,776,525,712,690,640,705,414,327,673,791,502,463,470,643,544,907,744,703,613,727,314,876,446,571,465,450,688,581,844,771,363,556,319,652,390,401,731,781,568,914,478,383,346,549,800,832,684,300,432,835,405,854,867,865,373,735,305,506,437,474,664,828,635,720,358,807,886,415,624,464,332,575,427,860,596,528,644,459,723,691,442,871,369,728,740,486,803,337,354,560,592,708,309,659,755,676,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA009-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n026.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 22:06:42 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.04/1.03 % [INFO] Parsing done (323ms).
% 2.04/1.04 % [INFO] Running in sequential loop mode.
% 3.13/1.43 % [INFO] eprover registered as external prover.
% 3.13/1.44 % [INFO] Scanning for conjecture ...
% 3.76/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 2782 axioms. Running axiom selection ...
% 4.68/1.85 % [INFO] Axiom selection finished. Selected 295 axioms (removed 2487 axioms).
% 5.17/1.94 % [INFO] Problem is propositional (TPTP CNF).
% 5.17/1.95 % [INFO] Type checking passed.
% 5.17/1.95 % [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 ...
% 13.17/3.52 % External prover 'e' found a proof!
% 13.17/3.52 % [INFO] Killing All external provers ...
% 13.17/3.52 % Time passed: 3026ms (effective reasoning time: 2477ms)
% 13.17/3.52 % Axioms used in derivation (295): clsarity_IntDef__Oint_34, cls_Nat_Onot__gr0_0, cls_OrderedGroup_Ojoin__0__eq__0_1, cls_Set_OCompl__subset__Compl__iff_1, cls_OrderedGroup_Oneg__less__iff__less_1, cls_OrderedGroup_Oneg__0__equal__iff__equal_0, cls_Power_Onat__zero__less__power__iff_2, cls_Nat_Onot__less0_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_Nat_Onat__add__left__cancel__less_1, clsrel_OrderedGroup_Olordered__ab__group__meet_1, cls_OrderedGroup_Oneg__le__iff__le_0, clsrel_OrderedGroup_Olordered__ab__group_3, cls_Nat_Onat__add__right__cancel_0, cls_IntDef_Oof__int__0__le__iff_0, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oordered__idom_12, cls_IntDef_Oof__int__0__less__iff_0, clsarity_IntDef__Oint_24, clsrel_OrderedGroup_Olordered__ab__group__join_3, cls_OrderedGroup_Oneg__0__le__iff__le_1, cls_OrderedGroup_Oneg__0__less__iff__less_0, cls_Nat_Omult__le__cancel1_1, clsrel_OrderedGroup_Opordered__ab__group__add_1, clsrel_Ring__and__Field_Oordered__idom_23, clsarity_IntDef__Oint_52, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_OrderedGroup_Opprt__eq__id_0, cls_OrderedGroup_Oadd__le__cancel__right_0, cls_OrderedGroup_Oneg__le__0__iff__le_1, cls_Nat_Oop_A_K_Omult__0_0, cls_OrderedGroup_Oadd__less__cancel__right_0, cls_IntDiv_Ozero__less__zpower__abs__iff_2, cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__idom_37, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13, clsarity_nat_40, clsrel_Ring__and__Field_Oordered__idom_17, 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_Oadd__is__0_0, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_NatBin_Oeq__0__number__of_1, cls_OrderedGroup_Oneg__meet__eq__join_0, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Oof__int__less__iff_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Oaxclass__abs__if_0, clsrel_OrderedGroup_Oab__group__add_0, cls_Nat_Omult__less__cancel2_1, cls_Nat_Omult__0__right_0, cls_Set_OCompl__eq__Compl__iff_0, clsarity_IntDef__Oint_0, clsarity_IntDef__Oint_38, cls_Set_OpsubsetI_0, cls_Set_Osubset__refl_0, cls_LOrder_Ojoin__idempotent_0, cls_Nat_Onat__add__left__cancel__le_0, cls_List_Ochar_Oinject_0, cls_OrderedGroup_Omeet__0__eq__0_0, cls_Nat_Omult__less__cancel1_1, cls_Nat_Oadd__gr__0_2, clsrel_OrderedGroup_Olordered__ab__group__abs_0, cls_Nat_Onat__add__left__cancel__less_0, cls_OrderedGroup_Oabs__eq__0_0, clsarity_nat_36, clsarity_IntDef__Oint_47, clsarity_IntDef__Oint_48, cls_Nat_Omult__le__cancel1_0, cls_IntDef_Oof__int__le__0__iff_1, cls_Set_Osubset__empty_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, clsrel_OrderedGroup_Olordered__ab__group_6, cls_Parity_Ozero__less__power__nat__eq__number__of_1, clsarity_IntDef__Oint_58, clsrel_OrderedGroup_Olordered__ab__group__abs_4, clsrel_Ring__and__Field_Oordered__idom_38, cls_Nat_Omult__less__cancel2_0, cls_Parity_Ozero__less__power__nat__eq__number__of_0, clsrel_Ring__and__Field_Oordered__idom_51, clsrel_Ring__and__Field_Oordered__idom_36, cls_OrderedGroup_Oadd__less__cancel__left_1, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Ring__and__Field_Oordered__idom_52, cls_OrderedGroup_Ozero__le__pprt_0, clsrel_OrderedGroup_Olordered__ab__group_0, cls_IntDef_Oof__int__less__iff_1, clsrel_OrderedGroup_Olordered__ab__group__join_17, cls_Nat_Oadd__is__0_1, cls_OrderedGroup_Oneg__0__less__iff__less_1, cls_OrderedGroup_Ojoin__0__eq__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_Nat_Omult__le__cancel2_2, clsrel_OrderedGroup_Olordered__ab__group__meet_5, clsrel_OrderedGroup_Olordered__ab__group_17, cls_Set_OCompl__subset__Compl__iff_0, clsarity_set_12, cls_IntDef_Oof__int__0__le__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, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_OrderedGroup_Oneg__le__iff__le_1, cls_Set_Oempty__subsetI_0, cls_List_Odrop__0_0, clsrel_OrderedGroup_Oab__group__add_1, clsrel_Ring__and__Field_Oordered__idom_11, cls_Ring__and__Field_Omult__cancel__left1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_6, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsarity_nat_37, cls_Nat_Omult__cancel2_0, clsrel_LOrder_Olorder_0, cls_Set_Osubset__antisym_0, cls_Nat_Onat__add__left__cancel__le_1, clsarity_set_14, cls_Nat_Omult__less__cancel1_0, clsarity_IntDef__Oint_37, clsrel_OrderedGroup_Opordered__ab__group__add_2, clsarity_nat_6, cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0, cls_NatBin_Oeq__nat__number__of_10, cls_OrderedGroup_Opprt__0_0, clsrel_OrderedGroup_Olordered__ab__group__abs_16, cls_Nat_Onat__0__less__mult__iff_1, cls_Set_Osubset__empty_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_OrderedGroup_Olordered__ab__group_1, clsrel_OrderedGroup_Olordered__ab__group__meet_15, clsrel_OrderedGroup_Olordered__ab__group_5, cls_Nat_Omult__cancel2_1, clsrel_OrderedGroup_Olordered__ab__group__abs_6, 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_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_NatBin_Oadd__nat__number__of_1, clsarity_IntDef__Oint_54, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_OrderedGroup_Olordered__ab__group__join_16, clsrel_Ring__and__Field_Oordered__idom_35, cls_OrderedGroup_Oadd__le__cancel__left_0, cls_OrderedGroup_Opprt__mono_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, cls_Nat_Oadd__gr__0_0, cls_OrderedGroup_Oabs__minus__cancel_0, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_OrderedGroup_Onprt__eq__0_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_Nat_Onot__add__less1_0, cls_OrderedGroup_Ozero__less__abs__iff_1, clsrel_OrderedGroup_Olordered__ab__group__abs_1, cls_Nat_Oadd__is__0_2, cls_OrderedGroup_Oadd__le__cancel__right_1, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0, clsrel_OrderedGroup_Olordered__ab__group_15, clsrel_Ring__and__Field_Oordered__idom_41, cls_Nat_Omult__cancel1_0, clsarity_IntDef__Oint_32, cls_OrderedGroup_Oabs__eq__0_1, cls_OrderedGroup_Oadd__less__cancel__right_1, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_OrderedGroup_Oabs__le__zero__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_2, clsarity_IntDef__Oint_22, cls_Nat_Omult__le__cancel2_1, clsarity_nat_20, cls_OrderedGroup_Oneg__less__0__iff__less_1, cls_Nat_Oadd__0__right_0, clsrel_Ring__and__Field_Opordered__semiring_4, clsarity_nat_5, cls_OrderedGroup_Oadd__less__cancel__left_0, cls_Power_Onat__zero__less__power__iff_1, cls_Set_OpsubsetE_0, clsrel_Ring__and__Field_Oordered__idom_8, clsrel_OrderedGroup_Olordered__ab__group__meet_3, cls_IntDiv_Ozero__less__zpower__abs__iff_0, cls_Nat_Onot__gr0_1, clsarity_IntDef__Oint_43, cls_OrderedGroup_Ominus__add__distrib_0, cls_Nat_Onot__add__less2_0, clsarity_set_13, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsarity_nat_9, cls_OrderedGroup_Oadd__0__right_0, cls_IntDef_Oof__int__eq__0__iff_0, cls_OrderedGroup_Oneg__less__iff__less_0, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__idom_4, clsrel_OrderedGroup_Olordered__ab__group__meet_16, clsarity_nat_35, cls_OrderedGroup_Oneg__0__equal__iff__equal_1, cls_IntDef_Oof__int__le__iff_1, cls_IntDef_Oof__int__le__0__iff_0, clsrel_OrderedGroup_Opordered__ab__group__add_13, cls_OrderedGroup_Oabs__0__eq_1, clsarity_IntDef__Oint_17, cls_OrderedGroup_Onprt__0_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_OrderedGroup_Olordered__ab__group_2, cls_IntDef_Oof__int__less__0__iff_1, cls_Nat_Omult__less__cancel1_2, cls_OrderedGroup_Oneg__equal__0__iff__equal_1, cls_IntDef_Oof__int__0__less__iff_1, cls_OrderedGroup_Oright__minus_0, cls_IntDiv_Ozero__le__zpower__abs_0, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_OrderedGroup_Opordered__ab__group__add_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, cls_Nat_Onat__add__left__cancel_0, cls_IntDef_Oof__int__0__eq__iff_1, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, clsrel_OrderedGroup_Olordered__ab__group__abs_2, clsarity_nat_13, clsrel_Ring__and__Field_Oordered__idom_34, cls_OrderedGroup_Oneg__equal__iff__equal_0, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsarity_nat_24, cls_List_Olexn_Osimps__1_0, cls_OrderedGroup_Oneg__le__0__iff__le_0, clsarity_IntDef__Oint_51, cls_OrderedGroup_Oadd__le__cancel__left_1, clsarity_set_0, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_Nat_Ole0_0, clsarity_nat_4, cls_OrderedGroup_Oneg__0__le__iff__le_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0, cls_NatBin_Oadd__nat__number__of_0, cls_Nat_Oop_A_L_Oadd__0_0, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_Nat_Oadd__gr__0_1, cls_Set_Onot__psubset__empty_0, cls_Nat_Ole__0__eq_1, clsarity_IntDef__Oint_50, cls_List_Ochar_Oinject_1, cls_OrderedGroup_Oabs__of__nonneg_0, clsarity_IntDef__Oint_12, clsrel_OrderedGroup_Opordered__ab__group__add_12, cls_OrderedGroup_Oneg__less__0__iff__less_0, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, clsrel_OrderedGroup_Olordered__ab__group__join_5, cls_Nat_Omult__le__cancel1_2, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Set_OpsubsetE_1, cls_Nat_Omult__le__cancel2_0, clsrel_OrderedGroup_Olordered__ab__group__meet_2, clsrel_Ring__and__Field_Opordered__comm__semiring_7, cls_IntDef_Oof__int__eq__0__iff_1, cls_OrderedGroup_Oabs__idempotent_0, cls_Set_Odouble__complement_0, cls_Nat_Omult__less__cancel2_2, cls_List_Odrop__upt_0, cls_NatBin_Oeq__number__of__0_1, cls_OrderedGroup_Oabs__le__zero__iff_1, cls_Nat_Omult__is__0_0, cls_List_Ochar_Osize_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0, 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_Power_Onat__zero__less__power__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_18, clsarity_set_15, cls_List_Odrop__drop_0
% 13.17/3.52 % No. of inferences in proof: 599
% 13.17/3.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3026 ms resp. 2477 ms w/o parsing
% 14.14/3.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.14/3.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------