%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV972-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 09:01:10 AM UTC 2026
% Result : Unsatisfiable 14.02s 4.55s
% Output : Refutation 15.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 447
% Syntax : Number of formulae : 895 ( 325 unt; 0 typ; 0 def)
% Number of atoms : 1755 ( 798 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 12138 ( 828 ~; 860 |; 0 &;10450 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 103 usr; 21 con; 0-8 aty)
% Number of variables : 3018 ( 0 ^;3018 !; 0 ?;3018 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(c_List_Olist__all2_decl,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(c_TypeRel_Owiden_decl,type,
c_TypeRel_Owiden: $i > $i > $i ).
thf(v_P_decl,type,
v_P: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(tc_String_Ochar_decl,type,
tc_String_Ochar: $i ).
thf(tc_Expr_Oexp_decl,type,
tc_Expr_Oexp: $i > $i ).
thf(v_Us_____decl,type,
v_Us____: $i ).
thf(tc_Type_Oty_decl,type,
tc_Type_Oty: $i ).
thf(c_WellTypeRT_OWTrts_decl,type,
c_WellTypeRT_OWTrts: $i > $i > $i > $i > $i > $o ).
thf(v_h_Ha_____decl,type,
v_h_Ha____: $i ).
thf(v_E_____decl,type,
v_E____: $i ).
thf(v_es_Ha_____decl,type,
v_es_Ha____: $i ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_Otake_decl,type,
c_List_Otake: $i > $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_Int_Onumber__class_Onumber__of_decl,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_List_Odrop_decl,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i > $i ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i > $i ).
thf(c_List_Otl_decl,type,
c_List_Otl: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(c_List_Osko__List__XCons__eq__append__conv__1__1_decl,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_List_Osko__List__Xappend__eq__Cons__conv__1__1_decl,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_List_Onth_decl,type,
c_List_Onth: $i > $i > $i ).
thf(c_List_Olist__update_decl,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_Type_Oty_OClass_decl,type,
c_Type_Oty_OClass: $i > $i ).
thf(c_Type_Oty_ONT_decl,type,
c_Type_Oty_ONT: $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_TypeRel_OMethod_decl,type,
c_TypeRel_OMethod: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_Expr_Oexp_OVal_decl,type,
c_Expr_Oexp_OVal: $i > $i > $i ).
thf(c_Expr_Oexp_OCall_decl,type,
c_Expr_Oexp_OCall: $i > $i > $i > $i > $i ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(c_Objects_Ohext_decl,type,
c_Objects_Ohext: $i > $i > $o ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_WellTypeRT_OWTrt_decl,type,
c_WellTypeRT_OWTrt: $i > $i > $i > $i > $i > $o ).
thf(c_Progress_OWTrt_H_decl,type,
c_Progress_OWTrt_H: $i > $i > $i > $i > $i > $o ).
thf(c_WellType_OWT_decl,type,
c_WellType_OWT: $i > $i > $i > $i > $o ).
thf(c_Conform_Oconf_decl,type,
c_Conform_Oconf: $i > $i > $i > $i ).
thf(v_sko__local__XIH__1_decl,type,
v_sko__local__XIH__1: $i > $i > $i > $i > $i > $i ).
thf(v_ha_____decl,type,
v_ha____: $i ).
thf(v_esa_____decl,type,
v_esa____: $i ).
thf(c_TypeSafe__Mirabelle_Osconf_decl,type,
c_TypeSafe__Mirabelle_Osconf: $i > $i > $i > $o ).
thf(v_la_____decl,type,
v_la____: $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(tc_Value_Oval_decl,type,
tc_Value_Oval: $i ).
thf(c_Conform_Osko__Conform__Xconfs__Cons2__1__2_decl,type,
c_Conform_Osko__Conform__Xconfs__Cons2__1__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Conform_Osko__Conform__Xconfs__Cons2__1__1_decl,type,
c_Conform_Osko__Conform__Xconfs__Cons2__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xlist__all2__append2__1__1_decl,type,
c_List_Osko__List__Xlist__all2__append2__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xlist__all2__append2__1__2_decl,type,
c_List_Osko__List__Xlist__all2__append2__1__2: $i > $i > $i > $i > $i > $i > $i ).
thf(v_v_____decl,type,
v_v____: $i ).
thf(v_C_____decl,type,
v_C____: $i ).
thf(c_Progress_OWTrts_H_decl,type,
c_Progress_OWTrts_H: $i > $i > $i > $i > $i > $o ).
thf(c_List_Osko__List__Xlist__all2__refl__1__1_decl,type,
c_List_Osko__List__Xlist__all2__refl__1__1: $i > $i > $i ).
thf(c_WellType_OWTs_decl,type,
c_WellType_OWTs: $i > $i > $i > $i > $o ).
thf(v_sko__local__XCallParams__Xhyps__2__1_decl,type,
v_sko__local__XCallParams__Xhyps__2__1: $i > $i > $i > $i > $i > $i ).
thf(v_sko__CHAINED__1_decl,type,
v_sko__CHAINED__1: $i > $i > $i > $i > $i > $i ).
thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2_decl,type,
c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2: $i > $i > $i > $i > $i > $i ).
thf(v_M_____decl,type,
v_M____: $i ).
thf(v_T_____decl,type,
v_T____: $i ).
thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1_decl,type,
c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1: $i > $i > $i > $i > $i > $i ).
thf(v_sko__local__XCallParams__2__1_decl,type,
v_sko__local__XCallParams__2__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xlist__all2__append1__1__1_decl,type,
c_List_Osko__List__Xlist__all2__append1__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(v_Ts_____decl,type,
v_Ts____: $i ).
thf(c_List_Osko__List__Xlist__all2__append1__1__2_decl,type,
c_List_Osko__List__Xlist__all2__append1__1__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Conform_Osko__Conform__Xconfs__conv__map__1__1_decl,type,
c_Conform_Osko__Conform__Xconfs__conv__map__1__1: $i > $i > $i > $i > $i > $i ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(645,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
= ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
= ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(1337,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__2__1 ) ) ) ) @ ( v_es_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallParams_I2_J_0) ).
thf(1454,plain,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__2__1 ) ) ) ) @ ( v_es_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(184,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(893,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Type_Oty_OClass )
!= ( B @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Oinject_0) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Type_Oty_OClass )
!= ( B @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(555,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(1295,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( B
= ( C @ ( E @ ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).
thf(762,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( B
= ( C @ ( E @ ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(1068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__list__update_0) ).
thf(1443,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(994,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(394,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wts_H__wts_0) ).
thf(1401,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(254,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(1073,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(90,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(655,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(677,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(861,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(436,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Obutlast ) )
= ( B @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__conv__take_0) ).
thf(1486,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Obutlast ) )
= ( B @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1205,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( A @ ( v_es_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( v_Us____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(449,plain,
! [A: $i] :
( ~ ( A @ ( v_es_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( v_Us____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons__number__of_1) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1275,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(445,axiom,
tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf_0) ).
thf(1507,plain,
tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(670,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__append_0) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(360,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCall_0) ).
thf(1327,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(389,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( F @ ( C @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__widens_0) ).
thf(1391,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( F @ ( C @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_lessequals ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Obutlast ) )
= ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__take_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_lessequals ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Obutlast ) )
= ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_2) ).
thf(1386,plain,
! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(377,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ c_List_Orev ) @ ( D @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).
thf(1366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ c_List_Orev ) @ ( D @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(327,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1254,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(181,axiom,
! [A: $i] :
( c_Type_Oty_ONT
!= ( A @ c_Type_Oty_OClass ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I20_J_0) ).
thf(885,plain,
! [A: $i] :
( c_Type_Oty_ONT
!= ( A @ c_Type_Oty_OClass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= B )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons__number__of_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= B )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(570,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
thf(1298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(719,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(162,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(838,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(424,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I12_J_0) ).
thf(1462,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_List_Onth ) @ hAPP ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).
thf(702,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_List_Onth ) @ hAPP ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(638,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) )
= ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__add_0) ).
thf(1147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) )
= ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(356,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__trans_0) ).
thf(1319,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(433,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I15_J_0) ).
thf(1479,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(211,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(969,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(448,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(267,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(1100,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(318,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).
thf(1232,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__length01_0) ).
thf(1415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__length01_0) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(1040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(363,axiom,
v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_I5_J_0) ).
thf(1334,plain,
v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(514,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osplit_0) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(340,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(821,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(21,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(492,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(426,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__hext_0) ).
thf(1465,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(402,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).
thf(1418,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(623,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(18,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(485,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__take_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(384,axiom,
( ( t_a @ ( v_P @ c_COMBI ) )
= v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1383,plain,
( ( t_a @ ( v_P @ c_COMBI ) )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__0_0) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(416,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).
thf(1447,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(866,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(371,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( C @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__widen_0) ).
thf(1351,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( C @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(409,axiom,
v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wte_0) ).
thf(1433,plain,
v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(396,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__def_0) ).
thf(1405,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= ( C @ ( D @ ( C @ ( B @ c_List_Onth ) @ ( A @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth_Osimps_0) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= ( C @ ( D @ ( C @ ( B @ c_List_Onth ) @ ( A @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__drop_0) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(527,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(877,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(105,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(692,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(1074,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(3,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(452,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(512,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(529,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).
thf(1306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(1199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(1153,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(428,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
thf(1438,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(387,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCallNT_0) ).
thf(1387,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons_H_1) ).
thf(894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(263,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_HOL_Oplus__class_Oplus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__drop_0) ).
thf(1091,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_HOL_Oplus__class_Oplus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__take_0) ).
thf(825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(373,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( E @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__2 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( F @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_2) ).
thf(1355,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( E @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__2 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( F @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(443,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( A @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( F @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__List__Xlist__all2__append1__1__2 ) ) ) ) ) @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__List__Xlist__all2__append1__1__1 ) ) ) ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_0) ).
thf(1502,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( A @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( F @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__List__Xlist__all2__append1__1__2 ) ) ) ) ) @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__List__Xlist__all2__append1__1__1 ) ) ) ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(729,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(405,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( L @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( K @ ( J @ c_Pair ) ) ) @ ( F @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( G @ ( E @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( H @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCall_0) ).
thf(1423,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( L @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( K @ ( J @ c_Pair ) ) ) @ ( F @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( G @ ( E @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( H @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(467,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__all_0) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(566,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(484,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(583,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(830,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(258,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(1079,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(5,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(456,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1017,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).
thf(615,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(1096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__take_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons__number__of_1) ).
thf(610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(274,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).
thf(1118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(989,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(33,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(519,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(578,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(107,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(697,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(1089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(1234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(272,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1111,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons__number__of_1) ).
thf(1227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(980,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(441,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wts__wts_H_0) ).
thf(1498,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(392,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ ( E @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( E @ ( D @ ( C @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).
thf(1397,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ ( E @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( E @ ( D @ ( C @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
thf(1493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(361,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__2 ) ) ) ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_4) ).
thf(1329,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__2 ) ) ) ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Conform_Osko__Conform__Xconfs__Cons2__1__1 ) ) ) ) ) @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__Cons2_1) ).
thf(1361,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Conform_Osko__Conform__Xconfs__Cons2__1__1 ) ) ) ) ) @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Oreplicate ) ) )
= ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(1182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Oreplicate ) ) )
= ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).
thf(1461,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(20,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(403,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrts__hext__mono_0) ).
thf(1419,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(188,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( B @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_2) ).
thf(901,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( B @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(679,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(970,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(358,axiom,
v_Us____ @ ( v_esa____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wtes_0) ).
thf(1324,plain,
v_Us____ @ ( v_esa____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(421,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( F @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__1 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( E @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_1) ).
thf(1456,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( F @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__1 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( E @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(1266,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(280,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(6,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(457,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(1246,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(266,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1099,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(985,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(1150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__refl_0) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] : ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(418,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(1451,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(123,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(738,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(390,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( C @ ( D @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( E @ ( C @ ( D @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_2) ).
thf(1393,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( C @ ( D @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( E @ ( C @ ( D @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(410,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( E @ ( D @ ( C @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_1) ).
thf(1434,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( E @ ( D @ ( C @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(341,axiom,
! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__refl_0) ).
thf(1286,plain,
! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1187,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(1167,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_0) ).
thf(953,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(182,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(888,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(132,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( J @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_0) ).
thf(765,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( J @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( B @ ( D @ ( C @ c_List_Oappend ) ) ) )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( B @ ( D @ ( C @ c_List_Oappend ) ) ) )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(314,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1219,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(435,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( F @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__2 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( E @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_2) ).
thf(1483,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( F @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__2 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( E @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(1273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
= ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
| ( C
!= ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A )
| ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
thf(1301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
= ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
| ( C
!= ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A )
| ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(59,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(573,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(126,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).
thf(750,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(447,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_1) ).
thf(1510,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(732,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(388,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( D @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_3) ).
thf(1389,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( D @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(189,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(207,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).
thf(958,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__drop_0) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(1256,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(545,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).
thf(1488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( D @ ( C @ ( B @ ( D @ ( A @ c_List_Obutlast ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__list__update_1) ).
thf(1428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
= ( D @ ( C @ ( B @ ( D @ ( A @ c_List_Obutlast ) @ c_List_Olist__update ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(283,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1139,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(353,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( F @ ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Conform_Osko__Conform__Xconfs__Cons2__1__2 ) ) ) ) ) @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__Cons2_2) ).
thf(1312,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( F @ ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Conform_Osko__Conform__Xconfs__Cons2__1__2 ) ) ) ) ) @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(787,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(114,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).
thf(713,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1058,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(1239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(10,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(466,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Objects_Ohext ) )
| ~ ( B @ ( C @ c_Objects_Ohext ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__trans_0) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Objects_Ohext ) )
| ~ ( B @ ( C @ c_Objects_Ohext ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(1258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(315,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( B @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_1) ).
thf(1224,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( B @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(1371,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(425,axiom,
tc_Type_Oty @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_Us____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_I4_J_0) ).
thf(1464,plain,
tc_Type_Oty @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_Us____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(397,axiom,
! [A: $i] :
( ~ ( A @ ( v_es_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( v_Us____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(1408,plain,
! [A: $i] :
( ~ ( A @ ( v_es_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( v_Us____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(1011,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(370,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( G @ ( E @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_Value_Oval @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__Cons2_3) ).
thf(1349,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( G @ ( E @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_Value_Oval @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).
thf(1122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(381,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__Xhyps__2__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallParams_Ohyps_I2_J_1) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__Xhyps__2__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(880,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(183,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(890,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(366,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I13_J_0) ).
thf(1339,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_1) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(67,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(594,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(359,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(1325,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_List_Osko__List__Xlist__all2__refl__1__1 ) @ ( C @ ( A @ c_List_Osko__List__Xlist__all2__refl__1__1 ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__refl_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_List_Osko__List__Xlist__all2__refl__1__1 ) @ ( C @ ( A @ c_List_Osko__List__Xlist__all2__refl__1__1 ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(232,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(1022,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(799,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Onth ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_List_Onth ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).
thf(1162,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Onth ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_List_Onth ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__0_0) ).
thf(700,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(34,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(520,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_es_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IH_0) ).
thf(1293,plain,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_es_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(249,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(1061,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(983,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(430,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__2__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallParams_I2_J_1) ).
thf(1474,plain,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__2__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(180,axiom,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(883,plain,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(440,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( B @ ( C @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__2 ) ) ) ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_4) ).
thf(1496,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( B @ ( C @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__2 ) ) ) ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(195,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).
thf(922,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(658,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(685,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(156,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(827,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(242,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(1044,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__drop_0) ).
thf(695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Obutlast ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__butlast_0) ).
thf(1445,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Obutlast ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(675,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(349,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).
thf(1304,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(427,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_5) ).
thf(1467,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(337,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1277,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ c_List_Onth ) @ hAPP ) @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__id_0) ).
thf(812,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ c_List_Onth ) @ hAPP ) @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(201,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).
thf(1472,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(1145,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(553,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(400,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).
thf(1413,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(256,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1076,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(308,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(1203,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(589,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(40,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(531,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(93,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( B @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_3) ).
thf(663,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( B @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(76,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(617,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(458,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).
thf(823,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(104,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(690,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Onth ) @ hAPP ) )
= ( tc_nat @ ( D @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__drop_0) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Onth ) @ hAPP ) )
= ( tc_nat @ ( D @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(378,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( E @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__1 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( F @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_1) ).
thf(1368,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( ( E @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__1 ) ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( F @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(317,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( F @ c_Objects_Ohext ) )
| ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__hext_0) ).
thf(1230,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( F @ c_Objects_Ohext ) )
| ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(226,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).
thf(1003,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(62,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(855,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(705,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(289,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1156,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(673,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(502,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(840,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(355,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__1 ) ) ) ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_3) ).
thf(1317,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append2__1__1 ) ) ) ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).
thf(1038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(64,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(585,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(576,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(374,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( A @ ( B @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( E @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ c_List_Osko__List__Xlist__all2__append2__1__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ c_List_Osko__List__Xlist__all2__append2__1__1 ) ) ) ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_0) ).
thf(1358,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( F @ ( D @ ( C @ c_List_Oappend ) ) @ ( A @ ( B @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( E @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ c_List_Osko__List__Xlist__all2__append2__1__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ c_List_Osko__List__Xlist__all2__append2__1__1 ) ) ) ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(1008,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(372,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_WellType_OWTs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCons_0) ).
thf(1353,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_WellType_OWTs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(404,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( C @ ( D @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).
thf(1421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( C @ ( D @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWTs ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__implies__WTrts_0) ).
thf(1459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWTs ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
= C )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
= C )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(524,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(399,axiom,
v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_esa____ @ ( v_M____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OCall ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_0) ).
thf(1412,plain,
v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_esa____ @ ( v_M____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OCall ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(313,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(1216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).
thf(1189,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(771,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(688,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(844,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(419,axiom,
v_h_Ha____ @ ( v_es_Ha____ @ ( v_Us____ @ ( v_P @ ( v_E____ @ v_sko__CHAINED__1 ) ) ) ) @ ( v_es_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1453,plain,
v_h_Ha____ @ ( v_es_Ha____ @ ( v_Us____ @ ( v_P @ ( v_E____ @ v_sko__CHAINED__1 ) ) ) ) @ ( v_es_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(385,axiom,
tc_Type_Oty @ ( tc_Type_Oty @ ( v_Us____ @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( v_Us____ @ ( v_P @ ( v_E____ @ v_sko__CHAINED__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
thf(1385,plain,
tc_Type_Oty @ ( tc_Type_Oty @ ( v_Us____ @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( v_Us____ @ ( v_P @ ( v_E____ @ v_sko__CHAINED__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Onth ) @ hAPP ) )
= ( D @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__append__length__plus_0) ).
thf(963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Onth ) @ hAPP ) )
= ( D @ ( C @ ( B @ c_List_Onth ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__Xhyps__2__1 ) ) ) ) @ ( v_es_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallParams_Ohyps_I2_J_0) ).
thf(1476,plain,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XCallParams__Xhyps__2__1 ) ) ) ) @ ( v_es_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(446,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Odrop ) ) @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).
thf(1508,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Odrop ) ) @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(434,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).
thf(1481,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(268,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(1101,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ c_List_Oappend ) ) )
= ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ c_List_Oappend ) ) )
= ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(367,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_5) ).
thf(1341,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(748,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(438,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( C @ ( E @ ( B @ ( D @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( B @ ( E @ ( D @ ( C @ ( A @ c_Conform_Osko__Conform__Xconfs__conv__map__1__1 ) ) ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__conv__map_1) ).
thf(1491,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( C @ ( E @ ( B @ ( D @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( B @ ( E @ ( D @ ( C @ ( A @ c_Conform_Osko__Conform__Xconfs__conv__map__1__1 ) ) ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Onth ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__append__length_0) ).
thf(1308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Onth ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(187,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(899,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(832,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(413,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( A @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( B @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( tc_Type_Oty @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_0) ).
thf(1440,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( A @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( B @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( tc_Type_Oty @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(929,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(210,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( H @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__idemp_0) ).
thf(967,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( H @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(950,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(391,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCons_0) ).
thf(1395,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(383,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_2) ).
thf(1380,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(140,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(790,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(411,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).
thf(1436,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(801,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(364,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__trans_0) ).
thf(1335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(247,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).
thf(1056,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(828,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_ONT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).
thf(635,plain,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_ONT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(41,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(532,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(1165,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( A
= ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).
thf(955,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( A
= ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(796,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(354,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( A @ ( F @ ( C @ ( B @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( tc_Value_Oval @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Conform_Osko__Conform__Xconfs__Cons2__1__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Conform_Osko__Conform__Xconfs__Cons2__1__1 ) ) ) ) ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__Cons2_0) ).
thf(1314,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( A @ ( F @ ( C @ ( B @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( tc_Value_Oval @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Conform_Osko__Conform__Xconfs__Cons2__1__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Conform_Osko__Conform__Xconfs__Cons2__1__1 ) ) ) ) ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1261,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(38,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(528,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ c_List_Olist_ONil ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
= ( D @ c_List_Olist_ONil ) )
| ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(442,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__1 ) ) ) ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_3) ).
thf(1500,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( E @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__List__Xlist__all2__append1__1__1 ) ) ) ) ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(850,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IH_1) ).
thf(1431,plain,
! [B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
| ~ ( B @ ( v_esa____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( v_h_Ha____ @ ( v_es_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__replicate_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(1120,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(25,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(501,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(1236,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(219,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).
thf(987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(382,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).
thf(1378,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(1505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__tl_0) ).
thf(1399,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(362,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_0) ).
thf(1331,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(1184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__append_0) ).
thf(543,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__append_0) ).
thf(560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(417,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).
thf(1449,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(592,plain,
! [B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1527,plain,
$false,
inference(e,[status(thm)],[645,1036,1337,629,760,1454,1031,893,481,479,1105,777,555,666,1295,1211,762,1290,1068,1443,994,1401,1073,1142,655,677,861,1486,1205,449,1137,550,1275,698,1063,538,1507,670,1310,533,814,1327,1001,1127,1391,782,1386,1366,1254,973,885,1046,724,1287,570,1298,719,785,1264,838,1279,934,1462,917,702,638,1087,1147,1319,1479,969,448,1100,1232,1415,1373,1040,1334,514,937,806,1283,821,492,1465,1418,623,485,834,1383,1020,734,1447,866,453,774,1351,1433,1405,1201,1242,507,527,877,692,1074,452,512,529,793,1306,1199,1153,810,1470,1438,661,1387,894,1091,825,1042,1355,598,1502,729,1423,467,852,493,757,682,1281,710,847,566,484,583,830,1159,461,1079,1027,456,842,874,650,1017,615,1425,1096,869,610,1118,499,989,519,578,697,1089,1234,1111,1227,980,1498,857,1397,1493,1329,1361,753,1182,1461,489,1214,1419,901,476,679,970,1324,1297,1456,1266,1131,1192,457,911,1246,1099,985,1150,1478,1249,1451,738,605,1393,1434,1170,1286,1187,1167,953,888,765,1054,906,1251,1103,1219,1483,1273,1301,573,965,750,1510,819,732,1389,1125,743,562,904,958,1403,1256,545,1488,1428,1139,1312,787,713,1058,1239,466,804,1258,1224,540,1271,1371,1464,947,1194,1408,1011,736,1349,996,1122,1376,1175,509,880,890,1080,1339,816,594,1325,1029,626,1344,1022,1177,799,1162,700,520,1293,668,932,1061,983,1474,883,1113,1496,505,922,658,685,521,768,827,1044,695,1066,1445,675,1304,1467,927,1277,812,939,1472,1145,553,836,1049,1413,473,1076,1203,1208,589,531,944,663,548,1134,648,617,516,458,823,690,640,1025,1070,1368,1230,557,1003,580,855,705,1156,673,502,840,1317,808,643,1038,585,1085,470,576,1358,613,1052,864,727,978,1008,859,991,1353,600,1421,1459,1180,1321,524,1412,1216,1189,771,1108,976,688,844,1453,1385,963,1476,1508,1481,1101,652,632,1244,1341,748,1491,568,914,1308,1077,899,832,536,716,1440,929,967,950,1395,1380,790,999,620,564,1436,801,1335,1056,828,635,532,1165,955,1346,796,1363,1314,1172,897,1410,1033,1197,1093,464,1129,1261,1268,528,908,1500,850,1431,871,1120,501,607,1236,987,596,1378,1505,1399,1331,486,1184,543,560,755,1449,592,496,708,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV972-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 15:16:21 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/1.36 % [INFO] Parsing done (375ms).
% 1.95/1.37 % [INFO] Running in sequential loop mode.
% 2.90/1.76 % [INFO] eprover registered as external prover.
% 2.90/1.77 % [INFO] Scanning for conjecture ...
% 3.39/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 506 axioms. Running axiom selection ...
% 4.37/2.17 % [INFO] Axiom selection finished. Selected 445 axioms (removed 61 axioms).
% 5.38/2.43 % [INFO] Problem is propositional (TPTP CNF).
% 5.38/2.45 % [INFO] Type checking passed.
% 5.38/2.46 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 14.02/4.54 % External prover 'e' found a proof!
% 14.02/4.54 % [INFO] Killing All external provers ...
% 14.02/4.54 % Time passed: 4002ms (effective reasoning time: 3161ms)
% 14.02/4.55 % Axioms used in derivation (445): cls_butlast__snoc_0, cls_IH_0, cls_sees__method__fun_1, cls_add__0__left_0, cls_exp_Osimps_I9_J_1, cls_append__eq__append__conv__if_3, cls_nth__list__update__neq_0, cls_power__0_0, cls_widens__Cons_2, cls_rev__swap_1, cls_Nil__is__rev__conv_1, cls_list__all2__append1_0, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_length__0__conv_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_calculation_I5_J_0, cls_take__eq__Nil_0, cls_Cons__eq__append__conv_2, cls_nth__Cons_H_0, cls_Cons__eq__append__conv_5, cls_nth__Cons__number__of_0, cls_le__diff__iff_0, cls_le__diff__conv_1, cls_list__all2__Cons_2, cls_eq__imp__le_0, cls_list__update__overwrite_0, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_list__all2__eq_1, cls_list__all2__append1_4, cls_append__self__conv_0, cls_drop__append_0, cls_zero__le__one_0, cls_take__0_0, cls_WTrtCallNT_0, cls_exp_Osimps_I81_J_0, cls_butlast_Osimps_I1_J_0, cls_eq__diff__iff_0, cls_replicate__empty_0, cls_tl_Osimps_I1_J_0, cls_take__Cons_H_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_rev__singleton__conv_1, cls_class__semiring_Osemiring__rules_I21_J_0, cls_list_Oinject_0, cls_add__increasing2_0, cls_CHAINED_0, cls_power__increasing_0, cls_WTrt_H__WTrts_H_Ointros_I13_J_0, cls_add__le__cancel__left_1, cls_add__is__0_0, cls_not__Cons__self2_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_widen__Class_2, cls_WTs__implies__WTrts_0, cls_rev__is__rev__conv_0, cls_append__eq__append__conv__if_6, clsarity_nat__Orderings_Olinorder, cls_diff__cancel_0, cls_add__imp__eq_0, cls_add__le__cancel__right_1, cls_take__add_0, cls_list__all2__append2_1, cls_nth__Cons_H_1, cls_add__leE_0, cls_append__eq__Cons__conv_4, cls_COMBI__def__raw_0, cls_self__append__conv_0, cls_comm__monoid__add_Omult__1__right_0, cls_wts__wts_H_0, cls_drop__0_0, cls_list__update__nonempty_1, cls_add__diff__assoc2_0, cls_eq__Nil__appendI_0, cls_comm__monoid__add_Omult__assoc_0, cls_add__cancel__21_1, cls_ty_Osimps_I20_J_0, cls_same__append__eq_0, cls_take__Cons__number__of_1, cls_append__Cons_0, cls_confs__conv__map_1, cls_length__butlast_0, cls_CallParams_Ohyps_I2_J_1, cls_sees__method__fun_2, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_butlast_Osimps_I2_J_1, cls_le__0__eq_0, cls_rotate1__length01_0, cls_drop__Cons__number__of_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_replicate__eq__replicate_0, cls_append__eq__append__conv__if_2, cls_diff__diff__right_0, cls_diff__diff__left_0, cls_append__eq__Cons__conv_0, cls_nth_Osimps_0, cls_widens__trans_0, cls_one__le__power_0, cls_diff__le__mono2_0, cls_tl__replicate_0, cls_add__le__mono_0, cls_diff__diff__cancel_0, cls_butlast__list__update_0, cls_CallParams_I2_J_1, cls_of__nat__le__iff_1, cls_list__all2__append2_5, cls_append1__eq__conv_1, cls_rev__drop_0, cls_rev__take_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_le__antisym_0, cls_add__right__mono_0, cls_order__eq__refl_0, cls_list__all2__rev_1, cls_power__0__left_0, cls_double__eq__0__iff_1, cls_widen__refl_0, cls_confs__Cons2_3, cls_right__minus__eq_0, cls_hext__trans_0, cls_of__nat__le__iff_0, cls_list__all2__rev_0, cls_list__all2__Cons_1, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_le__imp__diff__is__add_1, cls_hext__refl_0, cls_replicate__append__same_0, cls_list__update__beyond_0, cls_rev_Osimps_I2_J_0, cls_nth__via__drop_0, cls_take__1__Cons_0, cls_exp_Osimps_I9_J_0, cls_rev__singleton__conv_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_diff__add__inverse2_0, cls_nth__append__length__plus_0, cls_add__nonneg__eq__0__iff_0, cls_append__Nil2_0, cls_nat_Osplit_0, cls_widens__refl_0, cls_nat__add__left__commute_0, cls_trans__le__add2_0, cls_conf__widen_0, cls_append__self__conv2_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_CHAINED_1, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_add__left__mono_0, cls_self__append__conv2_0, cls_drop__tl_0, cls_Nitpick_Onat__case__def_1, cls_length__0__conv_0, cls_list__all2__append1_3, cls_self__append__conv2_1, cls_sees__method__fun_0, cls_WTrt__hext__mono_0, cls_append__eq__append__conv__if_4, cls_rotate__is__Nil__conv_0, cls_conf_0, cls_of__nat__0__le__iff_0, cls_Cons__eq__append__conv_3, cls_le__iff__diff__le__0_0, cls_rotate__rotate_0, cls_WTrt_H__WTrts_H_Ointros_I15_J_0, cls_append__is__Nil__conv_2, cls_diff__add__0_0, cls_length__list__update_0, cls_append__Nil_0, cls_class__semiring_Oadd__a_0, cls_append__eq__append__conv2_5, cls_wts_H__wts_0, cls_singleton__rev__conv_0, cls_append__eq__Cons__conv_5, cls_termination__basic__simps_I4_J_0, cls_trans__le__add1_0, cls_take__Cons_H_1, cls_of__nat__diff_0, cls_butlast__list__update_1, cls_drop__Cons__number__of_1, cls_termination__basic__simps_I3_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_butlast__conv__take_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_class__semiring_Oadd__0_0, cls_comm__monoid__add_Omult__commute_0, cls_rev__is__Nil__conv_0, cls_list__all2__Cons_0, cls_confs__Cons2_2, cls_replicate__app__Cons__same_0, cls_rotate__simps_0, cls_replicate__eq__replicate_1, cls_append__eq__Cons__conv_1, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_drop__1__Cons_0, cls_list__all2__refl_0, cls_add__cancel__21_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_rotate1__is__Nil__conv_0, cls_butlast__append_0, cls_list__all2__Nil_1, cls_self__append__conv_1, cls_take__append_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_append__eq__conv__conj_2, cls_list__update__code_I2_J_0, cls_list__all2__append2_4, cls_list__all2__appendI_0, cls_list__all2__append2_2, cls_rotate1__rotate__swap_0, cls_widens__Cons_0, cls_not__Cons__self_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_append__same__eq_0, cls_append__take__drop__id_0, cls_Nitpick_Onat__case__def_0, cls_zero__neq__one_0, cls_list__all2__def_0, cls_list__update__swap_0, cls_WTrtCall_0, cls_append__eq__conv__conj_0, cls_list__all2__rev1_1, cls_diff__self_0, cls_butlast__drop_0, cls_diff__is__0__eq_0, cls_natgb_Oadd__cancel_0, cls_drop__Cons_H_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_length__rev_0, cls_calculation_I4_J_0, cls_tl__take_0, cls_list__all2__append1_2, cls_drop__Nil_0, cls_append__assoc_0, cls_exp_Osimps_I80_J_0, cls_append__eq__append__conv__if_1, cls_add__diff__cancel_0, cls_butlast__append_1, cls_le__trans_0, cls_Pair__eq_0, cls_list__all2__Nil2_0, cls_Cons__eq__append__conv_0, cls_drop__butlast_0, cls_add__diff__assoc_0, cls_diff__add__assoc_0, cls_nat__add__right__cancel_0, cls_WT__implies__WTrt_0, cls_add__increasing_0, cls_ty_Oinject_0, cls_le__imp__diff__is__add_0, clsarity_nat__Orderings_Opreorder, cls_nat__diff__split__asm_1, cls_wt_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_right__minus__eq_1, cls_nat__diff__split_1, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_add__nonpos__nonpos_0, cls_diff__cancel2_0, cls_add__nonneg__eq__0__iff_1, cls_list__all2__dropI_0, cls_take__eq__Nil_2, cls_WTCons_0, cls_add__nonneg__nonneg_0, cls_empty__replicate_0, cls_append__eq__Cons__conv_2, cls_le__diff__conv_0, cls_le__diff__conv2_0, cls_replicate__add_0, cls_tl__append2_0, cls_list__all2__Nil_0, cls_rotate__simps_1, cls_rev__replicate_0, cls_drop__drop_0, cls_rev__eq__Cons__iff_1, clsarity_nat__Power_Opower, cls_drop__replicate_0, cls_conf__hext_0, cls_list__update__id_0, cls_nat__add__left__cancel__le_1, cls_Nat_Oadd__0__right_0, cls_eq__eqI_0, cls_nth__drop_0, cls_list_Osimps_I3_J_0, cls_rotate__is__Nil__conv_1, cls_le__add__diff__inverse_0, cls_le0_0, cls_list__all2__append2_3, cls_wt_H__wt_0, cls_le__eqI_0, cls_length__append_0, cls_le__add2_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_append__eq__conv__conj_1, cls_rev__is__Nil__conv_1, cls_list__all2__Cons1_3, cls_natgb_Oadd__r0__iff_0, cls_length__rotate1_0, cls_diff__self__eq__0_0, cls_ty_Osimps_I21_J_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_nat__add__left__cancel__le_0, cls_nth__Cons__number__of_1, cls_comm__monoid__add_Omult__left__commute_0, cls_list__all2__append1_5, cls_diff__0__right_0, cls_le__add__right__mono_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_confs__Cons2_1, cls_append__is__Nil__conv_1, cls_list__all2__append_0, cls_replicate__eq__replicate_2, cls_length__rotate_0, cls_confs__Cons2_0, cls_widens__Cons_1, cls_widen__trans_0, cls_diff__le__self_0, cls_list__all2__takeI_0, cls_diff__add__assoc2_0, cls_le__diff__conv2_1, cls_length__tl_0, cls_nat__le__linear_0, cls_WTrts__hext__mono_0, cls_Nil__is__rev__conv_0, cls_plus__nat_Oadd__0_0, cls_comm__monoid__add_Omult__1_0, cls_length__drop_0, cls_confs__widens_0, cls_list__all2__append_2, cls_exp_Osimps_I9_J_2, cls_Cons__eq__appendI_0, cls_WTrtCons_0, cls_confs__hext_0, cls_list__all2__append1_1, cls_WTrt_H__WTrts_H_Ointros_I12_J_0, cls_append__is__Nil__conv_0, cls_add__nonneg__eq__0__iff_2, cls_eq__eqI_1, cls_class__semiring_Oadd__c_0, cls_singleton__rev__conv_1, cls_list_Oinject_1, cls_nat__add__left__cancel_0, cls_add__le__mono1_0, cls_minus__nat_Odiff__0_0, cls_butlast_Osimps_I2_J_0, cls_append__eq__append__conv__if_0, cls_le__iff__add_1, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_Cons__eq__append__conv_4, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_add__is__0_2, cls_sees__method__fun_3, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_append__eq__appendI_0, cls_wtes_0, cls_wte_0, cls_rotate__length01_0, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_le__diff__iff_1, cls_rev__append_0, cls_butlast__take_0, cls_Cons__eq__append__conv_1, cls_take__Cons__number__of_0, cls_drop__take_0, cls_take__all_0, cls_WTCall_0, cls_sees__method__idemp_0, cls_add__mono_0, cls_Nil__is__append__conv_2, cls_nth__append__length_0, cls_diff__add__inverse_0, cls_diffs0__imp__equal_0, cls_rev__swap_0, cls_eq__iff__diff__eq__0_1, cls_tl__drop_0, cls_replicate__empty_1, cls_append__replicate__commute_0, cls_append__eq__append__conv__if_5, cls_class__semiring_Osemiring__rules_I24_J_0, cls_list__all2__eq_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_tl_Osimps_I2_J_0, cls_wt__wt_H_0, cls_diff__le__mono_0, cls_zero__le__power_0, cls_rev__eq__Cons__iff_0, cls_list__all2__append2_0, cls_take__drop_0, cls_add__leE_1, cls_that_0, cls_le__eqI_1, cls_class__semiring_Opwr__0_0, cls_impossible__Cons_0, cls_length__replicate_0, cls_nat__case__0_0, cls_le__iff__diff__le__0_1, cls_monoid__add__class_Oadd__0__right_0, cls_diff__commute_0, cls_le__add1_0, cls_drop__all_0, cls_le__add__diff_0, cls_drop__eq__Nil_0, cls_append__eq__Cons__conv_3, cls_eq__iff__diff__eq__0_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_COMBI__def_0, cls_widens__Cons_3, cls_Pair__eq_1, cls_rev__rev__ident_0, cls_add__le__cancel__left_0, cls_empty__replicate_1, cls_list_Osimps_I2_J_0, cls_power__decreasing_0, cls_zero__le__imp__of__nat_0, cls_list__all2__Cons2_3, cls_append1__eq__conv_0, cls_CallParams_I2_J_0, cls_drop__Cons_H_1, cls_not__one__le__zero_0, cls_le__refl_0, cls_CallParams_Ohyps_I2_J_0, cls_power__0__left_1, cls_list__all2__append_1, cls_add__le__cancel__right_0, cls_exp_Osimps_I3_J_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_list__update__nonempty_0, cls_IH_1, cls_power__mono_0, cls_list__all2__rev1_0
% 14.02/4.55 % No. of inferences in proof: 895
% 14.02/4.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4002 ms resp. 3161 ms w/o parsing
% 15.10/4.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.10/4.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------